Saffold, who spent his first three years playing left tackle for the Rams, landed awkwardly on his arm as he attempted to block Cleveland linebacker Paul Kruger.
The extent of the injury is unknown but Saffold walked to the locker room after the play. His return to the preseason game is doubtful.
Injuries for the Rams offensive line have loomed as a concern heading into this season. Saffold missed six games in 2012 with a knee injury and seven in 2011 with a concussion, ankle and pectoral injuries.