Donovan made the announcement during his weekly SEC teleconference on Monday.
Finney-Smith remains suspended after violating team rules and Frazier will not play because of an high-ankle injury, originally suffered during a 68-61 loss to Kentucky on Feb. 7.
Finney-Smith is second on the team in scoring at 12.9 points a game and leads the team with 5.8 rebounds per contest. Donovan said he will re-evaluate Finney-Smith's status before Saturday's game against Tennessee. He has already missed games against Vanderbilt and LSU because of the suspension.
Frazier leads the team in scoring with 13.2 points a game and will miss his fifth straight game. He also averaged 4.6 rebounds and 1.6 assists in the 23 games he has played this season.
Florida has lost four of its last five games and at 13-14 (6-8 SEC) is in danger of missing the NCAA tournament for the first time since 2009, after making the Final Four last season.
- Scooby Axson