Ozuna was at Marlins Park after the surgery wearing a soft cast.
"He needs to just get healthy," Marlins manager Mike Redmond said. "I'm sure we'll talk as an organization as to whether winter ball is an option for him. Then, he will, like everyone, will go into Spring Training and compete and try to make the team."
Ozuna injured his thumb while making a diving catch in the sixth inning of Monday night's 3-1 win over Colorado at Coors Field. His glove hand bent backward while he robbed Michael Cuddyer of a hit.
Ozuna played the rest of the game, and afterward, the Marlins -- unaware of the severity of the injury -- optioned him to Double-A Jacksonville.
Ozuna on Wednesday had his hand examined by a thumb specialist in Miami. It was revealed he had a torn ligament and an avulsion fracture.
Ozuna opened the season at Jacksonville, but he was called up the final day of April to replace Giancarlo Stanton, who went on the DL with a strained right hamstring.
"In Spring Training, we never talked about Ozuna coming to the big leagues and hitting fourth," Redmond said. "It never came up.
"He did a great job. You think about a kid who came to this team, right at the right time we needed a boost. He gave us that boost and went out there and played a great right field. Then he made a real easy transition to center field. He got big hits. He drove in a lot of runs for us. I think he brought some excitement to our lineup and to our team. It energized guys. It was perfect. It was just what we needed. He was as big a part of our June run as anybody."
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter