Cutler was injured in the second quarter of the Bears' 45-41 loss to Washington.
Also injured in the game was linebacker Lance Briggs, who is predicted to be out at least six weeks because of a fractured shoulder.
Cutler had completed almost two-thirds of his passes this season, throwing for 1,658 yards and 12 touchdowns so far this season.
Josh McCown, 34, is expected to fill in for Cutler as the Chicago quarterback. He was 14-of-20 for 204 yards and a touchdown against the Redskins after Cutler was injured.
The Bears, 4-3, have their bye week this weekend and then play NFC North division foes Green Bay and Detroit the two weeks after that.