Butler, in his fifth season out of Connecticut, suffered the injury when the hand struck the rim midway through the third period as he attempted to block a shot by Milwaukee's Ruben Patterson.
"I don't think I will suit up again this season," Butler told WUSA-TV in an interview Sunday night.
"Unfortunately, Caron is probably going to be out for a long time, maybe the season," Wizards Coach Eddie Jordan said. "We want to get further evaluation and then come up with an appropriate answer with all the results."
Butler, who averages 19.6 points per game and was a first-time all-star this season, is slated for an MRI on Monday morning.
If he is out for the rest of the season, his likely replacement in Washington's lineup would be fellow forward Jarvis Hayes.