Griffin underwent an MRI on the shoulder Monday.
Peter Schrager of Fox Sports and NFL Network first reported that Griffin could be out awhile.
Josh McCown is set to get the nod. After the game, Griffin moved slowly and admitted he was in pain after the game, the story said. The Browns offense hit a couple of big plays in Week 1 against a pretty good Eagles defense but overall struggled to finish drives and also had some drops. Josh Gordon should provide a boost with his return in Week 5.