He will reportedly undergo an MRI and receive a second opinion Monday.
The veteran picked up the injury in the third quarter and was unable to return after going into the locker room.
Talib appeared in all 15 games he was eligible for last season (he missed one game because of a suspension), and he maintained Pro Bowl status despite the Denver Broncos' slide down the standings.
In all, the 32-year-old finished his 10th NFL season with 31 total tackles, one interception and seven pass breakups.
Now in his first season with the Rams, Talib has no interceptions but nine tackles and two passes defended.
Unfortunately, the Rams secondary is suddenly thin as Marcus Peters suffered a calf injury Sunday, per ESPN's Adam Schefter. Sam Shields should be asked to pick up the slack on the boundary with Nickell Robey-Coleman also taking on more responsibility.