Cooper was injured in the second quarter while trying to catch a pass from quarterback Joe Flacco. He was taken to the locker room shortly after and ruled out with what the team called a head injury.
Cooper's injury is the latest blow to a Browns offense that has been decimated by injuries.
Cleveland has lost quarterback Deshaun Watson (shoulder), running back Nick Chubb (knee) and right tackle Jack Conklin (knee) to season-ending injuries. Left tackle Jedrick Wills Jr. (knee) is on injured reserve.
The Browns were starting their fourth quarterback this season in Flacco. Rookie Dorian Thompson-Robinson, who had started Cleveland's previous two games, is still in the concussion protocol.
Cooper had 3 catches for 34 yards before the injury. Coming into the game, he led the Browns with 47 receptions for 765 yards.