Bradford picked up the injury when scrambling towards the sideline in the fourth quarter of his side's 30-15 loss to the Carolina Panthers yesterday, falling awkwardly on his knee following a tackle by safety Mike Mitchell.
Rams coach Jeff Fisher refused to confirm the exact extent of the the injury, but did reveal that Bradford was in "significant pain" following the incident.
"I'm not going to deal with hypotheticals right now until I find out what really is going on with him," ESPN quotes Fisher as saying.
"It makes no sense to rush to a conclusion until we know. We'll get a medical and then we'll go from there. He was in significant pain on the sideline."
Kellen Clemens is the only other quarterback that the Rams have on either their active roster or practice squad.