Ozuna was injured Friday night when he dived back into the bag as he was being picked off.
Manager Mike Schildt said Ozuna will travel Sunday to St. Louis, where he'll be seen by a hand specialist. Schildt said the team believes surgery won't be required.
Ozuna was hitting .259 with 20 homers and 62 RBIs.
"He's a presence, and people had to game plan for him,'' Schildt said. "He's a residual guy in the lineup. He did his damage when he homered, 62 RBIs, but he also makes guys around him better.
"We're going to miss him, but we're going to have other opportunities for guys to step up."