Brewer hit his head on the ground while taking a sack from Sooners linebacker Kenneth Murray. He appeared shaken up but jogged off the field shortly after.
The junior was allowed to re-enter the game but was taken to the locker room for evaluation toward the end of the half.
Backup quarterback Gerry Bohanon has taken over under center for the remainder of the contest.
Brewer struggled to spark the Bears' offense prior to his injury, completing 3 of 6 passes for 15 yards.