"We're hoping that it will be the quickest course possible, but certainly [it's] not great news when you lose a guy that means what he's meant to this ball club and to baseball," Marlins manager Dan Jennings said.
Stanton paces the Majors in home runs (27) and RBIs (67), and he currently is second among National League outfielders in the All-Star voting.
The 25-year-old, who is putting together a National League MVP Award-caliber season, is facing surgery. Jennings confirmed the original prognosis is 4-6 weeks for full recovery. But the organization will know more after Stanton consults with team physician Dr. Lee Kaplan and a hand specialist.
"From what I've been told, it's better to have the surgical procedure, healing-wise," Jennings said. "But I think we'll have a better and clearer understanding after he visits today with the hand specialist."
Stanton winched in pain in the ninth inning after striking out against Pedro Baez. His hand was visibly swollen when he removed his batting glove after returning to the dugout. Stanton noted that he first tweaked his hand on a swing in the sixth inning, also during a strikeout.
Miami had just lost its fifth straight game when it was learned that Stanton would miss substantial time, including the All-Star Game.
"You lose your bat in the middle of the order that is leading baseball in RBIs," Jennings said. "So now it's upon us to pick it up. We can't feel sorry for ourselves. Injuries, unfortunately, are part of the game. We have to step it up. It'd be easy if you want to toss in the towel right now, or we're going to find out what kind of fighters that we have, and how we step up."
Miami placed Stanton on the disabled list on Saturday, and the club also optioned infielder Donovan Solano to Triple-A New Orleans. The team selected the contract of outfielder Cole Gillespie and recalled infielder Miguel Rojas from New Orleans.
Ichiro Suzuki will now see regular action in right field.
"It's going to change a little bit on how we have to play the game, because you can't sit back and wait on the big man to hit a two- or three-run home run," Jennings said. "But at the same time, there is still a lot of baseball left to be played, and we're going to have to step up and find a way."
Before suffering the fracture, Stanton was enjoying a remarkable June. The slugger hit .344 in the month with 12 homers and 23 RBIs.
The 12 blasts match a franchise record for most homers in any month. Stanton reached that number in May 2012, and Dan Uggla did it in May 2008.
Stanton is a two-time All-Star, and this season he has been on pace to be voted in as a starter for the first time in his career.
The injury means Stanton won't participate in the All-Star Game or Home Run Derby.
In 2012, Stanton was an All-Star reserve, but he didn't attend the game because he underwent right knee surgery days before the Midsummer Classic.
Stanton was an All-Star in 2014, and he started the game as the designated hitter.
If Stanton returns in August, he still will have time to challenge the Marlins' season home run record of 42, set by Gary Sheffield in 1996.
"You feel bad for him, because you see him day in and day out studying the pitching and doing all the right things," said Miami closer A.J. Ramos, Stanton's roommate. "For this to happen is really unfortunate."