Franklin completed 5 of 9 passes for 56 yards before leaving the game in the first quarter with a 6-0 Missouri lead. He was replaced by backup Corbin Berkstresser.
A team spokesman says Franklin would not return to the game. The junior sat out one game earlier this season after injuring his throwing shoulder in a home loss to Georgia.
Backup running back Marcus Murphy also left the game early with a dislocated right ring finger.
Starting middle linebacker Will Ebner also did not play, though the team did not say why.