The injury -- a non-displaced nasal fracture -- occurred in the final minute of Sunday's game when the forearm of Duke's Gerald Henderson smashed into Hansbrough's face as Hansbrough attempted a put-back.
Hansbrough is expected to play Friday when the Tar Heels face the Clemson/FSU winner in the ACC Tournament at noon. He'll wear a mask in practice this week and may wear it on Friday.
"I'm going to ask him to wear it the next couple of days," Williams said. "Whether we ask him to wear it in the game or not, we don't know yet."
Earlier in the game, in an unrelated play, Hansbrough also suffered an injury to his mouth which may result in dental work at a later date.