The 41-year-old, who won the 2009 edition of the Vuelta, suffered a heavy crash in Friday's seventh stage and subsequently abandoned the race.
His Movistar team said Valverde came through his operation successfully.
They said in a statement posted on Twitter: "@alejanvalverde has undergone surgery this Saturday morning for his right clavicle fracture after his fall in #LaVuelta21.
"The intervention, carried out by @DrEsparzaRos and Dr Javier Hernandez at the Hospital @GrupoHLA La Vega (Murcia), passed without complications."
No timescale for his recovery has been detailed.
Valverde, who began Friday's stage sitting fourth overall, attacked on the Puerto El Colloa, attempting to put his GC rivals onto the back foot, only to spin out of control on a difficult right-hand turn.
He crashed through a gap in the barriers and onto the lip of the hillside, avoiding tumbling further. Although he attempted to carry on after receiving treatment, Valverde was soon compelled to retire from the race.
Valverde posted on Friday evening that "it hurts to leave like this" as he came to terms with his fate, the race carrying on in his absence.
Three-time reigning champion Roglic crashed just before the line on Tuesday, having looked set to take the lead off Evenepoel, who has now held the red jersey for 12 stages of this year's event.
Roglic's chances of an unprecedented fourth straight Vuelta title are now over after the Slovenian elected to withdraw from the race, leaving Mas as Evenepoel's closest rival.
Yet the Spaniard was unable to close the gap on Wednesday as Evenepoel and his Quick-Step Alpha Vinyl team managed the red jersey group, with both riders collecting the same time after a 162-kilometre route from Aracena to Monasterio de Tentudia.
Rigoberto Uran claimed a breakaway win, sealing his first individual success at La Vuelta, meaning the 35-year-old has now won a stage at each of the Grand Tours.
Jesus Herrada led until just before the finish, with Uran timing his final attack to perfection to hold off Quentin Pacher and become the fourth different Colombian rider to win a stage at La Vuelta since the start of the 2019 edition.
Mas had to settle for 15th, one place behind Evenepoel, and knows his Movistar team will have to come up with something special to topple the Belgian in the race's final days.
"We go day by day, I think every day is super important. Yesterday you all saw the crash of Primoz. We need to be very focused," Mas said. "It's not nice when somebody crashes. He's a super rider, a super good person. I think it's s*** that Roglic is not here anymore.
"I don't know what we're going to do tomorrow, but if we have good legs and a good feeling, and the atmosphere in the team is super good, we have to do something, no?"
Evenepoel betters Merckx
He may hold a lead of over two minutes, but Evenepoel is not taking anything for granted, and delivered an expertly controlled ride to keep his rivals at bay.
"Pretty tough, it was not easy at all. Especially the run-in was really nervous and also a big road going quite steep. It looked easier on television than it was in real life," he said.
Evenepoel is the first rider to lead La Vuelta for 12 consecutive stages since 2019, when Roglic led for the final 12. The 22-year-old has now overtaken the great Eddy Merckx as fourth on the list of Belgians with the most days leading the race, after Gustaaf Deloor (32), Freddy Maertens (22) and Rick van Looy (13).
STAGE RESULT
1. Rigoberto Uran (EF Education–EasyPost) 3:42:28
2. Quentin Pacher (Groupama-FDJ) same time
3. Jesus Herrada (Cofidis) +0:02
4. Marc Soler (UAE Team Emirates) +0:15
5. Kelly Elissonde (Trek-Segafredo) +0:26
CLASSIFICATION STANDINGS
General Classification
1. Remco Evenepoel (Quick-Step Alpha Vinyl) 65:14:05
2. Enric Mas (Movistar) +2:01
3. Juan Ayuso (UAE Team Emirates) +4:51
Points Classification
1. Mads Pedersen (Trek-Segafredo) 349
2. Fred Wright (Bahrain Victorious) 149
3. Marc Soler (UAE Team Emirates) 133
King of the Mountains
1. Jay Vine (Alpecin-Deceuninck) 59
2. Richard Carapaz (INEOS Greandiers) 30
3. Thymen Arensman (Team DSM) 22
