Marlins president of baseball operations Larry Beinfest said the injury will likely put Ozuna out for the remainder of his first Major League season.
"It's highly doubtful and improbable that you'll see him again this season," Beinfest said.
"It's a minimum 6-8 weeks, and then you have to ramp up from there. So we're going to run out of time this season."
The Marlins optioned Ozuna to Double-A Jacksonville, along with second baseman Derek Dietrich, to open up space for top prospects Christian Yelich and Jake Marisnick after Monday's game. Ozuna said after the game he was OK, but the Marlins decided to send him to a hand specialist in Miami before he went to Jacksonville, and an MRI exam revealed the severity of the injury Thursday morning.
"It's surprising, because when we optioned him Monday night and asked him if he was OK, he stayed [in the game] and he said he was OK," Beinfest said. "We had a doctor check him out here and it was starting to swell and get a little bit irritated."
Dr. Patrick Owens of University of Miami Hospital will perform the surgery, which is scheduled for Friday. An avulsion fracture occurs when a piece of the bone tears away with the ligament, so the two injuries are related. Because the injury occurred in a big league game, Ozuna was placed on the Major League disabled list.
The 22-year-old suffered another serious injury late in Spring Training, when he broke his left wrist after colliding with the wall while making a catch.
Beinfest said winter ball and the instructional league could both be options for Ozuna, but that it's too early to decide where Ozuna will be sent as he tries to make it back to the big leagues. The primary focus is making sure he's ready for next year's Spring Training, Beinfest said.
"Like any young player, he's going to have to come out and make the team next year in Spring Training," Beinfest said. "Obviously we have some pretty spirited outfield competition.
"He did a great job. Our intention was for him to go down and work on some things offensively. Sure enough, it's just the way it goes. He makes really a game-saving catch and gets hurt and ends up on the DL instead of being able to work on some things that he needed to work on and probably come back [to the Majors] later this season."
With Ozuna going on the big league DL, it will impact his MLB service time, meaning he will likely qualify as a Super Two and be eligible for arbitration in 2016. If not for the injury, Ozuna would have returned to Double-A, where he opened the season, and he likely would not have had enough MLB service time to be arbitration-eligible until 2017.