"As we get closer, we'll have a better feel for how he's progressing," Bennett said of Anderson's timeline during Monday's ACC teleconference.
The school had estimated that Anderson would miss four to six weeks after injuring the finger on his shooting hand during the first half of the No. 3 Cavaliers' victory over Louisville on Saturday.
He left the game briefly, returning with his hand wrapped in ice and bandages.
With Selection Sunday a little more than a month away, it's likely that Virginia will have to at least wrap up the regular season without Anderson.
The Cavaliers play at NC State on Wednesday and have eight regular-season games remaining.
On a balanced Virginia team, the junior had emerged as the Cavaliers' go-to threat, hitting 43 percent from beyond the arc. He is averaging 13.2 points, 4.3 rebounds and 2.1 assists this season.
"The good news is it's nothing long term that will affect him as a player," Bennett said. "In the short term, of course, we're discouraged for him because he's having a heckuva year."