Butler sustained the injury before halftime of the Titan's 30-20 loss to the Panthers. He attempted to break up a pass from Carolina quarterback Kyle Allen that was intended for wide receiver Curtis Samuel.
Samuel came down with the reception in the end zone, but Butler remained on the field following the play. The Titans' medical staff helped Butler to the locker room as they attempted to stabilize his wrist.
Butler, a six-year veteran, has 32 total tackles, two interceptions and nine passes defensed this season. He returned a pick 23 yards to set up a touchdown during last week's win over the Tampa Bay Buccaneers.
LeShaun Sims started the second half in place of the injured Butler. Adoree' Jackson and Sims could see increased snaps in his absence.
The Titans will host the Kansas City Chiefs next Sunday.