Finney-Smith's status for Monday's game against Miami is uncertain. Finney-Smith led the seventh-ranked Gators (1-0) with 15 points in their 68-45 victory against William & Mary on Friday. He injured his hand in the first half, got it wrapped and finished the game.
Trainers initially diagnosed it as a sprain, but tests later revealed the fracture.
Florida is counting on Finney-Smith, the Southeastern Conference's Sixth Man of the Year last season, to take on a more prominent role this year.
Playing without him could create problems since the Gators already are down two frontcourt players. Chris Walker is suspended another game, and fellow forward Alex Murphy has to sit out nine more games under NCAA transfer rules.