He was placed on the 15-day disabled list Saturday.
"From everything we've got, the surgery was a success," manager Dan Jennings said, "and now you just go through the healing process and the rehab process to have him back."
The 25-year-old outfielder initially hurt the wrist on a swing and miss in the sixth inning of Friday night's game. Stanton's hand appeared swollen, and he said it hurt where he grips the bat. Stanton indicated the pain grew worse as the game progressed. He grimaced in pain with his final swing in the ninth inning and said that at-bat was "the icing on the cake."
Entering Saturday, Stanton led the majors with 27 homers and 67 RBIs. Last year he was in the thick of the home run race when a beaning ended his season Sept. 11, and he finished tied for second in the majors with 37 homers.
"It's very disappointing to see with the work he puts in,'' reliever A.J. Ramos said. "You see the year he's having, so you're definitely disappointed and you feel bad for him.''
Ramos said he went to dinner with Stanton on Friday night and that it was obvious the slugger was injured.
"His pain tolerance is ridiculous, so when you see him go down like that, you know something isn't right," Ramos said. "He had a pretty good idea [it was broken]."
The latest injury means Stanton will miss the All-Star Game. It's also a big blow to a team that is 15 games below .500.
The Marlins don't have anything close to Stanton ready to plug into his spot in right field. Ichiro Suzuki is expected to see a bulk of the action, but he is 41 and has little power (.275, one home run, 11 RBIs in limited duty prior to Saturday).
Miami also called up Cole Gillespie from Triple-A New Orleans. But Gillespie, 31, is a career .230 hitter in 113 career major league games, and he has never hit more than two homers in an MLB season.
The trade market is unlikely to yield much. The Marlins are more likely to dump salaries at this point than use a win-now approach.
"It's extremely disappointing," Marlins reliever Mike Dunn said. "He's one of the best players in the game. It's a big blow ... You can't really replace that kind of guy and the numbers (he produces). You just hope someone can come in and help out a little bit."
Stanton has 12 homers in June, tying the franchise record for any month. Despite his power surge, the Marlins had been woeful lately, batting .201 and averaging two runs a game over the past nine games through Friday.
"Now it's upon us to pick it up, and we can't feel sorry for ourselves,'' Jennings said. "It would be easy to toss in the towel right now or we're going to find out what kind of fighters we have and how we step up.''
Stanton signed a record 13-year, $325 million contract in November. At age 25, he has 181 career homers but because of injuries never has played more than 150 games in a season.
Information from ESPN.com contributor Walter Villa and The Associated Press was used in this report.