Vizcaino had the procedure on Wednesday in New York. He pitched in four games this season, getting one save and allowing one run in four innings for the National League East champs.
General manager Alex Anthopoulos has heard fans chanting at SunTrust Park for the team to sign free-agent closer Craig Kimbrel and bring him back to Atlanta, and Anthopoulos indicated the Braves are exploring all available options.
"There's been a ton of turnover from the beginning of camp to where we are today,'' Anthopoulos said Wednesday. "I think it goes without saying we're going to look to do what we can both internally and externally.''
Even before Vizcaino got hurt, there had been speculation that Kimbrel, who closed games last season for the World Series champion Boston Red Sox, would return to the Braves, his original team.
Anthopoulos declined to say if the team already has reached out to Kimbrel, as the Braves appear set in the immediate future to stay with A.J. Minter and other relievers to fill Vizcaino's role.
Atlanta ranks 24th in the majors with a 5.43 bullpen ERA and 25th with two saves. Minter is 0-2 with a 9.64 ERA, after allowing a career high-tying three runs in Tuesday's loss to the Arizona Diamondbacks.
"I just don't want to position it like I'm trying to foreshadow like great expectations -- 'Oh, he's working the phones. They're going to get someone tomorrow,'" Anthopoulos said. "But for me to sit here and say, 'We're good, everything's great, this too shall pass,' when Viz is down, that would be very insincere.''
The 28-year-old Vizcaino was put on the 10-day injured list a few days ago with right shoulder inflammation. Vizcaino, on a $4.8 million, one-year contract, has often been injured during his two stints with the club.
Dr. David Altchek performed the surgery. He cleaned up Vizcaino's labrum and removed scar tissue from the right shoulder joint.
"When he's right, he's one of the best there is,'' Braves manager Brian Snitker said of Vizcaino. "I felt for him. The kid cares. He wants to help this club and just wasn't able to do it."