Bujnoch missed three games this season because of the injury and arrived in Charlotte on crutches. He started 35 games in his Bearcats career and earned first-team All-Big East honors in 2012.
The news comes at a bad time for Cincinnati, which already is missing starting right guard Sam Longo, also a senior, due to a fractured ankle suffered against Louisville on Dec. 5.
The Bearcats (9-3) will have to rely on senior quarterback Brendon Kay, who has battled multiple injuries himself, against North Carolina (6-6). Cincinnati's offense has been fairly balanced under Tommy Tuberville, with the team rushing for 2,022 yards and passing for 3,766.
Cincinnati and North Carolina are set to kick off at 3:20 p.m. ET on Saturday. The game will be broadcast on ESPN.