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.
Saffold walked to the locker room after the play and did not return.
Rams coach Jeff Fisher initially indicated that Saffold would be all right during his halftime interview on the team's broadcast.
"Rodger is going to be OK," Fisher said. "He's going to be all right. X-rays were negative, so he'll be all right. He's going to be a little sore, but he'll be OK."
Saffold later returned to the field with his arm in a sling and Fisher was a bit more cautious in his description of the injury, telling the team's radio broadcast that Saffold "may miss a little bit of time," adding, "How much, I don't know."
Injuries for the Rams' offensive line have loomed as a concern heading into the season. Saffold missed six games in 2012 with a knee injury and seven in 2011 with concussion, ankle and pectoral injuries.