World number one Djokovic is returning to action this week, having taken time away from the tour since banking an 18th grand slam title by winning the Australian Open in February.
He received a first-round bye, but waiting for him in the last 32 is Sinner, who on Tuesday saw off 2017 Monte Carlo runner-up Albert Ramos-Vinolas 6-3 6-4, again illustrating the 19-year-old Italian's great potential.
World number 22 Sinner is the only teenager ranked inside the top 80 in the men's game and is coming off his first run to a Masters final, at the Miami Open.
The switch from hard courts to clay is one that Sinner is having to deal with, and seeing off a specialist on the surface in round one represents an impressive start, although facing two-time former champion Djokovic will be a step up.
"It's always good for me to see what I can do on clay," Sinner said, quoted on the ATP website. "Obviously, I am not in the best form on clay now for the first week.
"But I think today was a solid match from my side. It was not easy. He's not giving [away] one point, so you have to stay there the whole match. I think I played a good match from my side."
Greek fourth seed Stefanos Tsitsipas reached the last 16 with a 6-3 6-4 win over Russian Aslan Karatsev, but there was disappointment at the same stage for Italian eighth seed Matteo Berrettini, beaten 7-5 6-3 by Spain's Alejandro Davidovich Fokina. Those were the only second-round matches of the day.
Surprise Miami champion Hubert Hurkacz made a winning start, battling to a 6-3 3-6 6-3 first-round success against Italian qualifier Thomas Fabbiano to reach round two.
Roberto Bautista Agut, Grigor Dimitrov, Pablo Carreno Busta and Fabio Fognini each booked places in round two thanks to straight-sets wins.
Qualifier Federico Delbonis was a 7-5 6-1 victor over France's Adrian Mannarino, meaning the Argentinian faces the ultimate test in clay-court tennis next, a tussle with Rafael Nadal, the 11-time former champion in Monte Carlo.
Nadal has won all four of their previous matches, and their fifth encounter will immediately follow the Djokovic-Sinner match on Wednesday.
Seeded second and third respectively, Tsitsipas and Medvedev began Friday as the tournament's highest-ranked players following Novak Djokovic's shock exit, but both found themselves on the receiving end of comprehensive defeats.
World number three Tsitsipas was the victim as Fritz claimed his first victory over a top-10 ranked player on clay, ending the Greek's 12-match winning run at the competition with a 6-2 6-4 success.
Tsitsipas – who won the event in both 2021 and 2022 – was unable to contain Fritz as the American hit a series of huge winners en route to his third Masters 1000 semi-final.
Fritz will face Andrey Rublev in the final four after the fifth seed saw off the challenge of German qualifier Jan-Lennard Struff, posting a 6-1 7-6 (7-5) win.
Meanwhile, Medvedev came up short in his tussle with Rune, as the 19-year-old waltzed into his second Masters 1000 semi-final with a 6-3 6-4 triumph.
"It wasn't easy for sure, it's always tough to play Daniil," Rune said after his win. "It was actually my first time playing against him in a real match, but we've practised tonnes of times.
"I have huge respect for everything he's done. In the last week it was not easy to stop him, but I'm happy I managed to do it."
Rune now has a 10-8 record in meetings with his fellow top-10 players, and he will have to win another such duel to make the final, with Jannik Sinner his semi-final opponent.
Sinner needed 76 minutes to beat fellow Italian Lorenzo Musetti 6-2 6-2, and the 21-year-old now has the chance to reach his third Masters 1000 final, having previously finished as runner-up at two editions of the Miami Open.
Greek Tsitsipas, who defeated Andrey Rublev to triumph in Monaco last year, eased past second seed Alexander Zverev in the semi-final and repeated the trick with a 6-3 7-6 (7-3) victory over Davidovich Fokina.
The Spaniard beat Novak Djokovic and reigning Indian Wells Masters champion Taylor Fritz en route to his maiden ATP Tour final, and started well on Court Rainier III with an early break.
However, Tsitsipas found his rhythm with his ferocious forehand to break back before winning four of the next five games to take the lead.
The world number five, appearing in his fourth Masters 1000 final, then failed to serve out for the match at 5-4 up in the second set, but recovered in the tie-break to secure his first trophy of the season.
In doing so, Tsitsipas becomes the sixth player to manage consecutive Monte Carlo titles in the Open Era, while half of his eight tour-level titles have come on clay.
"I am very proud of myself," Tsitsipas said in his on-court interview. "Things weren't going well at one point, but I managed to stay composed to finish the match off.
"I am really proud with the belief I put in my game. Sometimes you doubt yourself, but it is always important to keep your head high."
Davidovich Fokina was aiming to become the first unseeded champion in Monte Carlo since Thomas Muster in 1992, and Tsitsipas acknowledged the 22-year-old made him fight to reclaim the trophy.
"He fought in moments I didn't expect him to fight," Tsitsipas said. "He can hit incredible winners out of nowhere and play unpredictably.
"But I was able to minimise that. I knew he would be a dangerous opponent but that is a great win for me. I think we will see great results from him in the future."
The third seed, who defeated Andrey Rublev to clinch the title in Monaco last year, produced a scintillating performance to beat the world number three 6-4 6-2 in Saturday's last-four encounter.
Tsitsipas will face world number 46 Alejandro Davidovich Fokina in Sunday's final, and the Greek said he will need to perform at an even higher level to defeat the 22-year-old, whose incredible run continued with a three-set win over Grigor Dimitrov in the final four.
"It was good," Tstispas told Amazon Prime Video of his semi-final win. "I don't know whether the long match [his three-set quarter-final win over Diego Schwartzman on Friday] gave me some rhythm, but I was able to play good tennis today. I'm happy with the level I was able to execute, and I came up with some good ideas on the court.
"I'm looking forward to the next one, I have a difficult opponent tomorrow, so I need to be ready and to take the best out of this one and move on.
"It's going to take a little bit more [to beat Davidovich Fokina], he's in a good rhythm. I've played him before, and he's a difficult opponent, I'm going to be as ready as possible, he's definitely improved and I'm going to have to produce the best tennis I can."
Davidovich Fokina, who has made headlines by eliminating Novak Djokovic and Indian Wells Masters champion Taylor Fritz during a thrilling run in the municipality, beat Dimitrov 6-4 6-7 (2-7) 6-3 earlier on Saturday, reaching his first ATP Tour final.
The unseeded Spaniard needed two hours and 43 minutes to wrap up his semi-final contest, and revealed that a bathroom break allowed him to reset his mind and clinch a hard-fought victory after he failed to serve out the second set at 5-4 up.
"I am so happy to be in the final, it's a dream come true to try to have the title," he said after the win.
"When I was a kid, I was dreaming about this day and it's come true, I'm so happy.
"In the second set I had my chances, I was so tight. But I went to the bathroom [after the second set] and I said to myself 'I want this'. Now I am in the final, I will enjoy, I have all the power with me."
The Greek star had lost his previous two finals at this level, with Rafael Nadal denying him in Toronto and Novak Djokovic beating him in Madrid.
However, he had the measure of Russian Rublev on the Monte Carlo clay on Sunday, breaking his opponent's serve three times and giving away nothing on his own delivery.
Tsitsipas, who lives in Monte Carlo, said he had experienced an "unbelievable week", declaring it was the pinnacle of his career to date.
"I can't describe the feelings right now," he said on Amazon Prime. "I'm overwhelmed by so many different emotions.
"It's incredible I'm able to be in the position I am, and I think we both deserved being in the final and put on an amazing fight and an amazing show.
"Generally I would consider it the week of my life so far. I knew he was going to be a very difficult opponent to face and there were a lot of nerves coming into that match.
"I've played him in the past, he always wants to bring the best out of us when facing each other."
Rublev beat 11-time Monte Carlo champion Nadal in the quarter-finals, but the 23-year-old could not hit the heights of that performance in the title match.
Tsitsipas, 22, said: "I'm just proud of the way I managed to behave and to be out on the court today.
"The clay-court season couldn't start better and it's the best thing right now, winning my first Masters 1000, and it's even more special doing it here on home soil in Monte Carlo and doing it on clay which is my favourite surface."
The pair, both three-time grand slam winners, enjoyed contrasting fortunes in their first-round matches against Tallon Griekspoor and Alex de Minaur.
Wawrinka, who has not played since Indian Wells last month, saw off the Dutchman in a 5-7 6-3 6-4 triumph, but Murray was routed by the Australian in a 6-1 6-3 loss.
"It was really important to stay calm with myself," Wawrinka said. "In the first round you need to find your game. I am happy to get through. It was important to fight until the end."
Roberto Bautista Agut saved a match point in the second-set tie-break as he fought back to overcome Filip Krajinovic to prevail 5-7 7-6 (12-10) 6-1.
Dominic Thiem is also through following a 6-1 6-4 win over Richard Gasquet but 11th seed Cameron Norrie is out after suffering a 6-3 6-4 loss to Francisco Cerundolo.
The former world number three made his comeback after more than a year out with a left foot injury that required two surgeries but fell to a 3-6 7-5 6-2 defeat to Alexander Bublik in the first round.
Wawrinka, who entered the tournament as a wildcard having slipped to 236 in the world rankings, came from a break down to take the opening set but fatigue eventually set in and he was eliminated after two hours and seven minutes.
"I think the body's getting much better," said Wawrinka, who lost in straight sets to Elias Ymer at a Challenger tournament in Marbella two weeks ago.
"I'm still far away from where I want to be, but I think I'm [going in] the right direction. I think today was a positive match. It was a tough loss, of course, but I'm happy with the way I was playing today.
"I was playing better, feeling better on the court physically. I spent a lot of mental energy to focus, to stay there as it was tough at the end. But I'm happy with what I have done."
Ninth seed Sinner was taken the distance by Coric before completing a 6-3 2-6 6-3 victory to advance to the second round.
Sinner took a medical timeout in the second set while he dealt with some apparent abdominal pain, but he was able to battle back and take the win.
Diego Schwartzman needed over three hours to come from behind and defeat Karen Khachanov 6-7 (5-7) 6-3 6-3, while his fellow Argentine Federico Delbonis set up a clash with second seed Alexander Zverev by besting Jaume Munar 6-4 3-6 6-4.
Reigning champion Stefanos Tsitsipas faces a meeting with Fabio Fognini in the second round after the Italian overcame Arthur Rinderknech 7-5 4-6 6-3.
There were also wins for Hubert Hurkacz, Pablo Carreno Busta, Marin Cilic, Alex de Minaur, Albert Ramos-Vinolas and Sebastian Korda.
Last year's runner-up Andrey Rublev, however, missed out on a last-eight spot after falling to a three-set defeat against Jannik Sinner.
World number three Zverev overcame Spain's Pablo Carreno Busta 6-2 7-5 to progress in Monaco, where he is seeking to win the sixth ATP 1000 title of his career.
"For the second clay-court match of the season, I can't complain too much," the 24-year-old second seed said on court after sealing the victory.
"Yes, I lost focus a little bit in the second set, but at the end of the day, he's somebody that can really play. I'm happy with a two-set win."
Tsitsipas (3) remains in contention for a second consecutive title in the principality after defeating Laslo Dere 7-5 7-6 (7-1) and will face off against 12th seed Diego Schwartzman for a semi-final spot after the Argentine defeated Lorenzo Musetti in a hard-fought three-set encounter.
There will be no repeat of 2021's final between Tsitsipas and Rublev, however, after the Russian fell to a thrilling 5-7 6-1 6-3 loss to ninth seed Sinner in the day's final contest.
The other seed to fall victim to a shock in the last 16 was world number seven Casper Ruud, losing 6-3 7-5 to Grigor Dimitrov, who will face Poland's Hubert Hurkacz in the last eight.
Finally, Novak Djokovic's conqueror Alejandro Davidovich Fokina cruised past David Goffin 6-4 6-1 to set up a quarter-final tie with the United States' Taylor Fritz, who bested compatriot Sebastian Korda – with whom he played doubles with in Monte Carlo – in straight sets.
Zverev, who is ranked third in the world - two places higher than Tsitsipas - fought back to defeat Jannik Sinner 5-7 6-3 7-6 (7-5) in his quarter-final match, denying his opponent another top-five seed scalp following his prior win over Andrey Rublev.
"It means a lot, definitely, especially [with] how this year has been going so far for me," said Zverev after a gruelling three hours on court.
"I've lost long matches like that, so I’m happy I won this one."
Tsitsipas also orchestrated a superb turnaround against Diego Schwartzman, prevailing 6-2 6-7 (3-7) 6-4.
The Greek had looked set for a last-eight exit at four games down in the final set, only to stage a dramatic comeback to keep his hopes of a first title since last May's Lyon Open alive.
"There was a moment in the match where I felt what I was doing wasn't working," Tsitsipas said.
"He had a massive lead and momentum in what he was trying to do. I just tried to stay in the match as much as I could and that worked out very well.
"I wasn't expecting much at that point being a double break down, so I relaxed at that point."
Schwartzman meanwhile will rue his inability to put the tie to bed, having already reached two ATP finals this year.
Grigor Dimitrov and Alejandro Davidovich Fokina will face off in the other semi-final.
Bulgarian Dimitrov beat off Hubert Hurkacz in another final-set tie-break, winning 6-4 3-6 7-6 (7-2).
Fokina, who eliminated Novak Djokovic in the second round, turned over Indian Wells champion Taylor Fritz in another comeback result, triumphing 2-6 6-4 6-3.
