The world number one cut short his quarter-final against Holger Rune in the French capital during a second-set tie-break after he lost the opener 6-3 on Friday.
Alcaraz stated after his retirement that it is too early to say whether he will be able to play in the prestigious season-ending tournament in Turin which starts on November 13.
The US Open champion said: "I don't know if I'll make it to the Masters Cup [ATP Finals]. Right now I have to do some tests to see how I am before going to Turin.
"I am focused on trying to improve my abdomen and trying to be 100 per cent in Turin."
The Spaniard felt there was no point in taking any chances.
He added: "At the end of the set, I felt bad. My abdomen was getting bad and I preferred to retire to see it and take care of it.
"I can't stretch. I couldn't serve well, I couldn't hit my forehand and when I turned the body I feel pain, I feel the abdomen in all the movements.
"I was playing thinking about it and feeling the pain, so it was better to withdraw."
Rune will face Felix Auger-Aliassime in his first ATP Masters 1000 semi-final, with both players finishing the season strongly.
Auger-Aliassime beat Frances Tiafoe 6-1 6-4 for his 16th consecutive win to set up a repeat of a final in Basel that the Canadian won last weekend.
The world number two is aiming to become the first player to successfully defend the Barcelona crown since Rafael Nadal won three in a row between 2016 and 2018.
And though run close by Davidovich Fokina, the reigning champion has now reeled off six sets without reply, taking his overall record at the ATP 500 event to 8-1.
The Spaniard, who is now 9-1 against his fellow countrymen since the start of 2022, will play Dan Evans in the last four. The Briton came from behind to defeat 15th seed Francisco Cerundolo 2-6 7-5 6-3.
They are joined by Stefanos Tsitsipas, whose quest for a first title of the campaign continues after a commanding 6-4 6-2 victory over eighth seed Alex De Minaur.
The second seed, who was runner-up at this event in 2018 and 2021, sealed the deal in one hour and 21 minutes to claim his ninth successive win against the Australian.
His reward is a showdown with Lorenzo Musetti, who received a walkover into the last four following Jannik Sinner's withdrawal.
Over in Munich, reigning champion Holger Rune booked his semi-final place with a dominant 6-2 6-4 win over Cristian Garin.
The world number seven, who is now 7-0 in this event, will play Christopher O'Connell. After defeating Alexander Zverev earlier in the week, the Australian qualifier built on his momentum by seeing off Flavio Cobolli 7-6 (7-5) 4-6 6-3.
Second seed Taylor Fritz also advanced in straight sets with a 6-3 6-4 victory over former world number three Dominic Thiem, who overcame eighth seed Marc-Andrea Huesler earlier in the day.
Fritz's semi-final opponent will be Botic van de Zandschulp after the fourth seed saw off Marcos Giron 7-6 (7-5) 6-3.
Alcaraz, who triumphed at last week's Indian Wells Open, beat the 76th-ranked Serbian 6-0 7-6 (7-5) in one hour and 32 minutes.
The 19-year-old Spaniard hit 26 winners compared to Lajovic's eight, while Alcaraz also sent down three aces on a 75 per cent first serve percentage.
Alcaraz won the first frame to love in 32 minutes, registering his fourth career bagel at ATP Masters 1000 level, equaling the most by a teenager alongside Rafael Nadal.
The world number one will face 2023 Australian Open semi-finalist Tommy Paul in the fourth round after the American got past 20th seed Alejandro Davidovich Fokina 6-3 7-5.
Third seed and 2022 Miami Open finalist Casper Ruud blew a first-set lead to lose 3-6 6-4 6-4 to Botic Van De Zandschulp.
The Dutchman improved his head-to-head record against Ruud to 3-1 with his first-ever top five win, with the Norwegian left to lament converting only two of 15 break points.
Ninth seed Taylor Fritz progressed into the fourth round with a 6-4 6-4 win over Denis Shapovalov, improving his head-to-head record against the Canadian to 4-5. Fritz committed only eight unforced errors and did not face one break point.
Jannik Sinner maintained his excellent hard-court form with his 18th win this season on the surface, as he defeated Grigor Dimitrov 6-3 6-4 in one hour and 28 minutes. The Italian 10th seed will be Andrey Rublev in the next round.
Sixth seed Rublev needed less than an hour to get past Miomir Kecmanovic 6-1 6-2, while compatriot Daniil Medvedev advanced via a walkover against Alex Molcan due to a right hip injury.
Seventh seed Holger Rune cruised past Diego Schwartzman 6-4 6-2, while Finland's Emil Ruusuvuori got past Taro Daniel 6-3 7-6 (7-3).
Reigning US Open champion Alcaraz eased past Bagnis 6-0 6-2, firing 12 winners and three aces for the match, committing only 11 unforced errors.
The Spaniard won the first set in 24 minutes, marking the first time he has won an opening frame 6-0 at an ATP Masters 100 event. It was also the first bagel he has dished out since beating Bagnis in Umag last year.
"I knew that I needed to be focused for my first match," Alcaraz said after his win, having triumphed in Indian Wells last week. "To start a new tournament is never easy, different conditions.
"I have to be ready to get used to these new conditions, but I was really focused on the match from the beginning, and I'm happy with the way that I played. I try to improve every day."
Alcaraz will face Dusan Lajovic after he beat 30th seed Maxime Cressy 6-4 7-6 (7-2), having knocked off Andy Murray in the first round.
Zverev was the highest seed to bow out on Friday, going down 6-0 6-4 to Japan's Taro Daniel, who beat world number four Casper Ruud last month in Acapulco.
Daniel triumphed in 73 minutes against the German, hitting 17 winners and committing only two unforced errors for the match, while Zverev gave up 18.
The Japanese wild card will meet Emil Ruusuvuori in the third round after the Finn beat 22nd seed Roberto Bautista Agut 6-4 7-6 (7-5) to open up that section of the draw.
Third seed Ruud also had few problems getting past Ilya Ivashka 6-2 6-3 to set up a clash with Botic van de Zandschulp after his three-set win over Alexei Popyrin.
Sixth seed Andrey Rublev overcame J.J. Wolf 7-6 (7-3) 6-4, having been broken in the opening game of what was a tight contest.
Jannik Sinner beat Laslo Djere 6-4 6-2, marking his 16th win out of 20 appearances at the Sunshine Double (Indian Wells and Miami), with only three other players – Novak Djokovic, Alcaraz and Hubert Hurkacz – having as many wins within their first 20 matches.
Ninth seed Taylor Fritz defeated fellow American Emilio Nava 6-4 6-1, and will face Denis Shapovalov in round three after he beat Guido Pella 6-3 3-6 6-3.
American 16th seed Tommy Paul came from a set down to beat Marc-Andrea Huesler 5-7 6-3 6-4, while seventh seed Holger Rune beat Martin Fucsovics 6-3 7-5.
Alcaraz won 6-3 6-3 over Thanasi Kokkinakis in one hour and 18 minutes in his opening match of the event, which also marked his return from a fortnight out with a hamstring injury.
The Spaniard, who reached the semi-finals at Indian Wells last year, could return to the number one ranking with victory at this year's event in the absence of Novak Djokovic.
Alcaraz hit 21 winners against the 94th-ranked Australian, dropping only one point on serve in the opening frame.
Fritz went a set down against 2023 Australian Open quarter-finalist Ben Shelton but eventually prevailed 4-6 6-4 6-3 in one hour and 53 minutes.
Both players were excellent on serve throughout the contest, with Fritz earning a break in the 10th game of the second set to tie up the match, before swooping again in the sixth game of the decisive frame.
Veteran Andy Murray moved into the third round with a 6-4 6-3 win over Radu Albot, with the Briton to take on countryman Jack Draper next. Draper won 6-4 6-2 over 24th seed Daniel Evans.
Murray had been set to face 15th seed Pablo Carreno Busta in the second round, but he withdrew due to a muscle injury, allowing Albot into the draw as a lucky loser. Murray's win was his first in straight sets since October.
Seventh seed Holger Rune won 7-5 6-3 over American Mackenzie McDonald, progressing to face Stanislas Wawrinka after he toppled 26th seed Miomir Kecmanovic 7-6 (10-8) 6-4.
Ninth seed Hubert Hurkacz got past Australian Alexei Popyrin 6-3 6-3, setting up a third-round clash with 17th seed Tommy Paul who won 6-3 6-3 over Jan-Lennard Struff.
Eighth seed Felix Auger-Aliassime won 7-6 (7-5) 6-4 over Pedro Martinez, while 11th seed Jannik Sinner got past veteran Richard Gasquet 6-3 7-6 (7-2).
Last week's Mexican Open champion and 16th seed Alex de Minaur was the highest seed to be knocked out on Saturday after a 6-4 6-2 loss to Martin Fucsovics.
The highly rated Spanish teenager eventually downed the German wildcard 3-6 6-1 7-6 (7-3).
Kuhn, ranked 259 in the world, was aggressive early on against Alcaraz, and was rewarded with the first set.
But the 19-year-old – playing as top seed in an ATP Tour event for the first time – rallied to ease through the second set, before being made to work much harder to clinch the win on a tie-break.
Alcaraz will now play Filip Krajinovic in the second round after the Serbian also won in a third-set tie-break against Sebastian Baez 6-1 4-6 7-6 (8-6).
Three seeded players crashed out on Tuesday in straight sets, with third favourite Diego Schwartzman losing against Emil Ruusuvuori 7-5 6-4, sixth seed Nikoloz Basilashvili beaten by Aslan Karatsev 6-4 6-0, and eighth seed Holger Rune going down 7-6 (10-8) 7-5 to Tallon Griekspoor.
Fourth seed Pablo Carreno Busta eased through against Luca Nardi 6-2 6-1, while there were also wins for Fabio Fognini, who sealed his 400th career victory, as well as Daniel Elahi Galan, Borna Coric and Francisco Cerundolo.
At the Swiss Open in Gstaad, sixth seed Cristian Garin lost 6-3 6-4 to Yannick Hanfmann and seventh favourite Hugo Gaston fell to Dominic Thiem despite winning the first set, losing 1-6 6-1 7-6 (9-7).
Elsewhere, Frenchman Richard Gasquet beat Roberto Carballes Baena 7-5 6-4, while his compatriot Benoit Paire retired hurt when a set and a break down against Elias Ymer.
A tight game between Swiss pair Dominic Stricker and Marc-Andrea Huesler saw the former prevail 6-7 (2-7) 7-6 (7-2) 6-4, and an all-Spanish affair was similarly close as Jaume Munar defeated Bernabe Zapata Miralles 6-3 3-6 7-5.
There were also wins for qualifiers Juan Pablo Varillas and Nicolas Jarry against Lorenzo Sonego and Thiago Monteiro respectively.
Auger-Aliassime saw off the US Open champion in just 82 minutes as he won 6-4 6-3 to take his unbeaten run to 12 matches.
The Canadian was in irresistible form on Saturday, with his shot placement in decisive moments proving far more consistent and lethal than his counterpart, hitting 23 winners to Alcaraz's eight.
Twenty-two-year-old Auger-Aliassime is still fighting to qualify for the ATP Finals for the first time and victory in Sunday's final will move him up to sixth in the rankings having won each of his two previous tournaments in Antwerp and Florence.
"It's amazing," Auger-Aliassime said. "I never expected it, when I was in Florence three weeks ago, or after the US Open. I'm just really happy that all my work is coming together.
"I've always believed that I can play this way, that I can be consistent in that way, but one thing is to believe and the other is to actually do it. It's nice to feel that way, it's nice to come out on the court and win that many matches in a row. So hopefully this is just the beginning of seeing me play this way."
Rune awaits after the Dane beat Roberto Bautista Agut 7-6 (7-1) 7-6 (10-8) despite being 6-2 down in the second-set tie-break. He will move into the top 20 for the first time as a result of that win.
The final of the Vienna Open will be contested by Daniil Medvedev and Denis Shapovalov, who came through their respective semis in straight sets.
Top seed Medvedev was exceptional against Grigor Dimitrov, with the Russian's serve proving especially important in his 6-4 6-2 win.
Medvedev won 87 per cent of points on his first serve to leave Dimitrov frequently struggling for momentum, and the former world number one recognised that impact.
"The serve is probably the most important shot in tennis," he said. "I was lacking it a little bit this season, I was doing too many double faults. Sometimes in important moments my serve could have been a little bit better. I was working a lot with my coach to try and find this rhythm [again], and so far I'm serving good here. I'm really happy about it and that's also why I'm playing so good."
Shapovalov ultimately romped to an impressive win over Borna Coric.
A tight first set was followed by the Croatian getting bageled as Shapovalov won 7-6 (7-4) 6-0 to reach his second final of the year.
Alcaraz took just under an hour and 40 minutes to overcome his fellow Spaniard and friend 6-3 6-4, getting 67 per cent of his first serves in and winning 77 per cent of those.
Carreno-Busta struggled to keep the US Open champion at bay, facing 12 break points in all, and although he saved nine of them, his defiance was ultimately in vain.
"It is difficult to play against a friend like Pablo," Alcaraz said on-court after his win on Friday. "Every day we go and have dinner, lunch, together. Every week and we train together, so it is difficult to play against him.
"I also support him and want him to win every match. On court, there are no friends. You have to be focused and go for the match and that is what I did."
Alcaraz will face third seed Felix Auger-Aliassime in the final four after the Canadian defeated Alexander Bublik 6-2 6-3.
The other semi-final will see Roberto Bautista Agut play Holger Rune after the Spaniard beat Stan Wawrinka 7-5 7-6 (7-5) and the Danish teenager defeated Arthur Rinderknech 7-6 (7-0) 6-2.
In Austria, top seed at the Vienna Open Daniil Medvedev beat Jannik Sinner 6-4 6-2 to advance to the last four, where he will play Grigor Dimitrov after the Bulgarian overcame Marcos Giron 6-3 4-6 6-4.
The winner of that contest will face either Denis Shapovalov, who beat Dan Evans 6-3 6-3, or Borna Coric after the Croatian came through against Hubert Hurkacz 6-4 6-7 (2-7) 7-6 (7-5).
The world number one suffered an internal oblique muscle tear during a Paris Masters quarter-final against Holger Rune on Friday.
Alcaraz retired early in a second-set tie-break after losing the opening set 6-3 in the French capital.
The US Open champion on Saturday revealed it will take him six weeks to recover from the injury, so Taylor Fritz will take his place in the ATP Finals in Turin next week.
Teenager Alcaraz will also be unavailable for Spain's bid to win the Davis Cup on home soil, with the prestigious event getting under way on November 22 in Malaga.
He posted on Instagram: "After my withdrawal yesterday and having been evaluated by my medical team, Dr Juanjo Lopez and Juanjo Moreno, unfortunately this is the result of my injury: an internal oblique muscle tear in the left abdominal wall with an estimated recovery time of six weeks.
"Unfortunately I won't make the ATP Finals or the Davis Cup Finals. It is tough and painful for me to miss these two events, which are so important to me, but all I can do is be positive and focus on my recovery. Thank you for the support!"
The 19-year-old became the youngest player to top the ATP rankings after winning his maiden major title at Flushing Meadows in September and ends a magnificent season with a record of 57 wins and 13 defeats.
He has won five ATP Tour titles in 2022, with Masters 1000 triumphs in Miami and Madrid along with his finest hour in New York.
The two-time Wimbledon champion, who opted for some extra match play following his first-round exit at Queen’s Club last week, was beaten 6-4 6-4 at the Giorgio Armani Tennis Classic.
Murray moved well on court against his 20-year-old opponent but could not capitalise on his chances, notably four break points in the sixth game of a tight opening set.
A double fault from the 36-year-old gifted Rune the first break of the contest and he was ultimately unable to battle back after dropping serve in the first game of the second.
Murray had won 10 successive matches in claiming back-to-back grass-court titles in Surbiton and Nottingham before suffering an early exit at Queen’s at the hands of Alex De Minaur.
“It’s great obviously to play these sorts of matches a few days out from Wimbledon,” Murray said in his on-court interview after his defeat.
“He’s one of the top players in the world, so you get to see exactly where your game is at. There are things to work on but it keeps you very sharp.
“I would have liked to have done a little bit better but I can start from here and build on this.”
Two days before discovering his fate as an unseeded player in the Wimbledon draw, the Scot was given a serious workout on a warm afternoon in west London.
A fashion show provided the pre-match entertainment on the north bank of the river Thames and it was the energetic Rune who proved to be the more stylish on court.
Like many of the catwalk models, the Dane had his baseball cap on backwards and he exuded the confidence of a player who has recently won four ATP titles, including defeating Novak Djokovic in the 2022 Paris Masters final.
Former world number one Murray grew into the encounter and showed glimpses of his grand-slam winning best throughout with soft hands at the net, powerful groundstrokes and some delightful lobs.
However, Rune often had the edge when it mattered in an exhibition match lasting around an hour and 40 minutes.
Murray, currently ranked 39 by the ATP, was finally broken in the ninth game following one of a handful of double faults across the high-profile exhibition match.
Rune wasted little time in wrapping up the set and then swiftly backed it up with a further break en route to another impressive victory of his fledgling career which underlines his credentials as an outsider for glory at SW19 in the coming fortnight.
The two-time former Wimbledon champion has opted for some extra match play following his first-round exit to Alex De Minaur at Queen’s Club last week.
World number six Rune, 20, reached the semi-finals of the cinch Championships before also losing to De Minaur and should provide strong opposition for Murray at the exhibition event.
Hurlingham frequently attracts the world’s best players and will also host world number one Carlos Alcaraz, top British player Cameron Norrie and defending Wimbledon champion Novak Djokovic.
The Serbian, who will bid to equal Roger Federer’s tally of eight titles at the All England Club, faces exciting American star Frances Tiafoe on Thursday.
Third seed Auger-Aliassime beat French qualifier Gregoire Barrere 6-4 6-3, while Medvedev earned a 6-2 6-2 victory against Dutchman Botic van de Zandschulp.
Despite being the higher-ranked of the two at present, Canadian Auger-Aliassime has a 0-4 career record against Russian Medvedev.
Those losses include a painful defeat from two sets up in the 2022 Australian Open quarter-finals, and a US Open semi-final knockout blow in the previous season.
It is a record that is all the more surprising considering Auger-Aliassime has wins over Novak Djokovic, Rafael Nadal, Roger Federer, Andy Murray and Carlos Alcaraz to his name.
Auger-Aliassime sits eighth on the ATP ranking list, three places clear of former number one Medvedev, who is relishing their clash on Friday.
Medvedev said on Amazon Prime: "Felix is a top player. He won here last year and played amazing at the end of last season. I'm looking forward to a tough match, and hopefully I can be at my best.
"He's going to take his opportunities. He's going to go for it when he has the chance. So I will need to be at my best and everything has to be better."
Top seed and Australian Open runner-up Tsitsipas was beaten 6-4 6-3 by Jannik Sinner, with last week's Open Sud de France champion winning in an hour and 21 minutes to set up a quarter-final against Stan Wawrinka.
It was Sinner's first career win over a top-three opponent. The Italian held a 0-8 record against such opponents coming into this match.
Fourth seed Holger Rune is also out after retiring hurt while 6-4 4-0 down to Dutch wildcard Gijs Brouwer, who advances to play compatriot Tallon Griekspoor.
Australian Alex de Minaur advanced to the final eight with a 7-5 3-6 6-3 win over American Maxime Cressy, earning a shot at Grigor Dimitrov next.
The Canadian had not won any of his eight career finals before this season, but he has now come through four of five in 2022.
Three of those have been in Auger-Aliassime's past three tournament entries, as he followed up successes in Florence and Antwerp by beating Holger Rune on Sunday.
Rune had himself won last time out against Stefanos Tsitsipas in the Stockholm final, but he was brushed aside by Auger-Aliassime 6-3 7-5.
The world number nine threatened to wrap up the victory in double quick time as he raced through the opener, with Rune responding in the second set to drag the match out to 100 minutes.
Auger-Aliassime fended off a break point early in the second and two more later in the set, protecting his serve throughout and then going on the offensive.
The fourth of four break opportunities at 5-5 was seized, and Auger-Aliassime – fresh from beating world number one Carlos Alcaraz – served out the match at the third attempt.
The 22-year-old has never previously made the season-ending Finals but moved ahead of Andrey Rublev with his latest success.
Rublev prevailed 6-3 3-6 6-3 4-6 7-6 (11-9) in a three-and-a-half-hour thriller against the Dane on Monday to progress to the quarter-finals of the Australian Open.
The Russian salvaged two match points to force a tie-break at the end of the fifth set, but found himself staring down the barrel of an exit from the season's first major as Rune cruised into a commanding lead.
Yet Rublev won nine of the next 11 points and, at the third attempt, sealed a remarkable victory when a shot that hit the net cord trickled just over.
"Yes, I was lucky," Rublev said in his post-match press conference.
"I started to think it's over, for sure. Somehow... I was able to start to play with much more focus."
Asked how he maintained his self-belief, Rublev quipped: "I was not believing."
"Beginning of the fifth set, I was completely frozen. Inside I was thinking that I cannot [win]. I cannot move. I cannot hit.
"I was thinking it's over. He's playing much better than me. He deserves to win. He's going for the shots. He's doing something that normally I am supposed to do if I want to win the match.
"I let it go. Somehow the stress that I had, I was able to relieve it. At the end of the match I played much better than during the rest of the match."
During his on-court interview, Rublev said: "I was never able to win matches like this, this is the first time I've won something like this.
"At a very special tournament, to be in a quarter-final, it's something I'll remember all my life. I'm shaking!"
Rublev has qualified for his second Australian Open quarter-final, and his seventh at a grand slam. However, he has lost all of those matches.
The world number six, seeded fifth in Melbourne, has won three successive matches that have gone the distance, a career-first. Now, he will meet nine-time champion Novak Djokovic, who defeated Alex de Minaur in straight sets.
"I don't know," Rublev replied when asked if Djokovic was unbeatable.
"Novak is very tough player to beat, especially in the slams.
"He has the best experience to win these matches. He's one of the best in history. The only chance I have is if I play my best tennis, just fight for every ball, and that's it. That's the only chance."
Former Wimbledon runner-up Berrettini beat American Mackenzie McDonald 3-6 7-6 (7-2) 6-3 at the hard court event, while Musetti came through 6-3 6-4 against Serbian Miomir Kecmanovic.
Providing Berrettini is healthy to participate in the final, the tournament looks set to deliver a crowd-pleasing trophy match, but it was touch and go whether the Rome native would get through the McDonald match.
"I don't even know how I did it," Berrettini said. "I wasn't feeling very good. I asked for the physio because my foot was hurting. It happened so many times in my career that I had to fight through so many things, not just thinking about the tennis ball."
He added, quoted by the ATP: "I didn't want to retire. My team told me, 'I think you should stop'. But I tried and I found a way."
Berrettini and Musetti have never gone head-to-head before. Berrettini has won two titles this year, both on grass, in Stuttgart and at London's Queen's Club, while 20-year-old Musetti scooped his maiden ATP title on clay in Hamburg.
At the European Open in Antwerp, Sunday's final will see American Sebastian Korda tackle Canadian Felix Auger-Aliassime, in a battle of two in-form players.
Korda was runner-up last week in Gijon, while Auger-Aliassime took the title in Florence, adding to his Rotterdam triumph from February.
Korda wrestled his way past a recently resurgent Dominic Thiem, scraping a 6-7 (4-7) 6-3 7-6 (7-4) victory, before Auger-Aliassime was given a mighty battle by veteran Frenchman Richard Gasquet, winning through in two tight sets, 7-6 (7-2) 7-6 (7-3) his margin.
Like Berrettini and Auger-Aliassime, Greece's Stefanos Tsitsipas has a third title of the year in his sights this weekend.
Tsitsipas swept through to the final of the Stockholm Open with a 6-2 6-2 win over Finland's Emil Ruusuvuori, setting up a clash with 19-year-old Danish player Holger Rune.
For Rune, there was no such straightforward path into the final as Alex de Minaur pushed him all the way, with the Australian eventually edged out 4-6 7-6 (7-1) 7-5 after two hours and 50 minutes.
Borges created a remarkable 20 break points, converting only five but still comfortable against his 61st-ranked opponent.
That sets up a clash with number one seed Alcaraz, who beat Pablo Carreno Busta in the 2022 final.
Ben Shelton's 7-5 6-4 success over countryman Mackenzie McDonald means he will take on Casper Ruud, while Bernabe Zapata Miralles will play Roberto Bautista Agut in an all-Spanish second-round affair after earning a routine 6-2 6-2 win over unfancied Attila Balazs.
Meanwhile, Emil Ruusuvuori beat Alexander Bublik in Barcelona for a second straight year to set up a second-round meeting with fifth seed Frances Tiafoe.
At the BMW Open in Munich, 2022 winner Holger Rune will open his defence against Yannick Hanfmann after the German battled from a set down to beat Thiago Monteiro 6-7 (3-7) 7-6 (7-5) 6-2.
Marcos Giron reached the second round with a 6-1 5-7 6-2 victory over Roberto Carballes Baene.
World number one Alcaraz and sixth seed Rune played doubles together when they were 14 and now the duo were the first men under 21 to face each other in a Wimbledon quarter-final in the open era.
It was the first time they had met at a grand slam, the start of a rivalry which could last for 10 or 15 years, and it was the Spaniard who came out top with a 7-6 (3) 6-4 6-4 victory on Centre Court.
Just six days separate the pair – Rune being the older – and as they headed into a first-set tie-break there was virtually nothing to choose between them either.
Alcaraz had hit 12 winners to Rune’s 13, both had made 12 unforced errors and both had won a total of 38 points.
Both had also double-faulted once, but Rune picked the wrong time to add to that particular tally to hand Alcaraz the advantage in the tie-break, which he went on to win with a stunning backhand return.
They exchanged further blows until 4-4 in the second set when Rune netted a simple overhead, and Alcaraz punished a second serve with another pin-point return to secure the first break of the match.
With England captain Ben Stokes watching in the crowd, it was Rune’s title hopes that were turning to ashes.
The weary Dane was given a warning for a time violation and was promptly broken for 3-2 in the third.
Rune saved a match point on his own serve but could not get near Alcaraz’s as the top seed wrapped up victory in two hours and 20 minutes.
Alcaraz, still a relative grass-court rookie despite his win at Queen’s Club a fortnight ago, said: “Honestly it’s amazing for me, a dream since I started playing tennis, making good results at Wimbledon, such a beautiful tournament.
“To be able to play a semi-final here… I think I’m playing at a great level, I didn’t expect to play such a great level on this surface so for me, it’s crazy.
“At the beginning I was really nervous playing a quarter-final and playing against Rune, someone the same age and playing at a great level. But once you get to a quarter-final there are no friends, you have to focus on yourself and I did great in that.”
Alcaraz will play Russian third seed Daniil Medvedev, who beat him in the second round two years ago when he really was a novice on grass, in the semi-final.
“We played two times, once here at Wimbledon,” added Alcaraz. “It’s going to be a tough one.
“But right now I’m going to enjoy this moment. You don’t play a semi-final every year.”
Paris-born American Cressy won 7-5 6-7 (3-7) 7-6 (7-4) in a little over two and a half hours, countering 10 double faults with 15 aces on his way to victory.
Rune, the Danish 19-year-old who sits ninth in the world rankings, had won his three previous matches against Cressy, including a second-round clash at the Australian Open last month, but he could not extend that dominance at the indoor event in Montpellier.
It means Cressy faces second seed Sinner, a player he lost to at a low-level tournament in Lexington in 2019, their only past meeting.
Sinner beat 18-year-old French wildcard Arthur Fils in Saturday's first semi-final, ending the teenager's eye-catching run with a 7-5 6-2 victory.
Fils had beaten Richard Gasquet and Roberto Bautista Agut on his way to the last four but found world number 17 Sinner was more than his match.
Last year saw Sinner reach just one ATP final, taking a title on clay in Umag, after making it through to five title matches in the 2021 season.
He had his best year at the grand slams, however, reaching quarter-finals at three of the four majors.
Cressy recognises the threat posed by the Italian, saying in an on-court interview: "Jannik Sinner is an incredible player, just like Holger Rune and everyone else in the tournament. I believe you've just got to bring your 'A' game every time and I'm really looking forward to it."
Competing well in France has been pleasing for Cressy, who is set to climb from 51st in the rankings and into the top 40 on Monday.
"I lived and grew up here, and I'm extremely happy," Cressy said.
Djokovic – who saw a three-year visa ban lifted in November – was playing with Vasek Pospisil in the doubles, and the duo lost 4-6 6-3 10-5 to Tomislav Brkic and Gonzalo Escobar on Monday, but the fans in attendance chanted "Novak" as they welcomed him back following his absence from last year's Australian Open.
The Serbian will face Constant Lestienne in the first round of the men's singles, but second seed Felix Auger-Aliassime is already out after he lost to Alexei Popyrin.
Auger-Aliassime struggled throughout as his Australian opponent, ranked 120th in the world, put in a crowd-pleasing performance to go through 6-4 7-6 (7-5).
Another young star, Holger Rune, is also out after the fifth seed was beaten 2-6 6-4 6-4 by Yoshihito Nishioka.
Quentin Halys set up a potential second-round clash with Djokovic after beating Jordan Thompson in straight sets, while Miomir Kecmanovic, Jack Draper, Roman Safiullin and Thanasi Kokkinakis all progressed.
It was also a bad day for seeds at the Maharashtra Open in Pune, with Alex Molcan beaten 6-2 6-4 by Laslo Djere and Jaume Munar losing 6-4 7-5 to Tallon Griekspoor.
Dutchman Griekspoor will now play Marco Cecchinato after the Italian overcame Nikoloz Basilashvili, and Roberto Carballes Baena set up a last-16 clash against top seed Marin Cilic by defeating fellow Spaniard Bernabe Zapata Miralles.
Filip Krajinovic did make it through a tussle with home favourite Sumit Nagal to set up a meeting with Michael Mmoh, while Benjamin Bonzi will face third seed Emil Ruusuvuori after beating Tseng Chun-hsin.
The Serb broke his Russian opponent twice as he cruised to the opening set, and though Safiullin took the 21-time grand slam champion to a tie-break in the second, Djokovic's class showed as he won the tie-break 7-3 to ensure his place in Sunday's decider.
It was far from plain sailing for Djokovic, who conceded the tension in the second set was hard to handle.
Djokovic said: "I think it was a very competitive match, especially in the second set.
"I must say I was quite emotional on the court today in the second set, there was a lot of tension, and that was also due to his aggressive style of tennis. Big serves, and when he has time, he's so solid from the forehand and backhand corner.
"I knew that I had to stay very strong, and that he was definitely going to raise his level in the second set, which happened. I was serving for the match and played a couple of loose points, but credit to him for fighting back. It was an enjoyable evening on the court for sure."
Marin Cilic secured his spot as Djokovic's final opponent with a comfortable straight sets triumph over Constant Lestienne.
The Croatian second seed served 14 aces as he eased to victory in under two hours, winning 11 out of his 12 first-serve points en route to a 7-5 6-3 win.
Holger Rune is into the Sofia Open final after Jannik Sinner was forced to retire through injury with the Dane leading 5-7 6-4 5-2.
Sinner won the opening set but lost the second, and with Rune just one game away from winning the match, the top seed chose to retire with ankle pain, putting an end to his hopes of winning three straight titles in Sofia.
Rune will face Marc-Andrea Huesler in the final, after the world number 95 upset fourth seed Lorenzo Musetti.
The first set went to a tie-break as neither could find a break of serve, though Musetti found two in the tie-break to help him to a 5-1 lead.
However, the Italian surrendered the next six points as Huesler pulled off an incredible comeback to take the first set.
The second set was another tight affair as both held serve after serve, but Huesler finally found a crucial break to prevail 7-6 (7-5) 7-5.
