Bradford was struck down by a first-quarter hit from defensive lineman Armonty Bryant before eventually limping off.
The severity of the injury is not known but Bradford, entering his fifth season in the NFL, missed nine games last season with an injury to the same knee.
Bradford had completed just 4 of 9 passes for 77 yards when he exited. The Rams kick of their regular season against the Minnesota Vikings on Sept. 7.
(Writing by Jahmal Corner; Editing by Ian Ransom)