Wilkins has been limited due to strep throat for the past couple of weeks.
"He's doubtful," Bennett said on Friday. "Didn't do anything today."
Wilkins, a 6-foot-7 junior, started 28 games for the Cavaliers this season. He's the team's leading rebounder at 6.0 per game and also averaged 6.8 points.
Wilkins' minutes have dropped off since late February. He has played 23 minutes or fewer in each of the last six games. He played just five minutes against UNC Wilmington on Thursday, and 14 minutes against Notre Dame in the ACC tournament.
"This virus is hanging on," Bennett said. "He's lost some weight and just can't. He pushed for about four or five minutes, and that was it. He pretty much didn't have anything left and was having some trouble. He's doubtful for the game. I'm not expecting him to play. But you never know."
Virginia has played smaller in Wilkins' absence, going with four and five guards on the floor at the same time. Against Florida, Bennett will have to rely more heavily on big men Jack Salt and Mamadi Diakite.