Jones' finger will be placed in a splint, and the team left open the possibility that he could return to the court earlier with a protective splint.
Jones had been sidelined since Jan. 12 with a bone bruise in his right knee. He is averaging 6.3 points and shooting 58% from the field in 31 games (eight starts) for the Bulls.
Chicago already is without guards Lonzo Ball (knee) and Alex Caruso (wrist). Caruso had wrist surgery on Monday, and Ball is scheduled to have knee surgery later this week. They both also have a recovery time of six to eight weeks.