Coach Jimbo Fisher said the sophomore could be out until spring after he tore cartilage during the win against Wake Forest.
Coker won't be available for the bowl game and that week of practices, with Fisher noting, "It's six weeks non-weight bearing to let that heal."
Coker threw for 250 yards with one interception and a 102.78 quarterback rating in seven appearances this season.
Redshirt freshman Sean Maguire will now back up Heisman Trophy candidate Jameis Winston as freshman John Franklin moves up to the No. 3 quarterback slot. Florida State had planned to redshirt Franklin, but Fisher will use him if needed.