"He's going to be out for some time right now," Rams coach Sean McVay said Tuesday. "So that's a big loss for us."
Cooper suffered the injury late in the third quarter during a punt return.
McVay said Cooper was undergoing further evaluation to determine if surgery would be necessary.
"He's just got some loose fragments in there. It's a pretty serious ankle sprain is probably the best way I can put it," McVay said. "However you cut it, with just the type of player that he is and just the specific position that he plays, it's going to limit him for at least a few weeks at a minimum."
Further complicating the situation, backup Michael Thomas suffered a groin injury Monday playing on special teams. McVay said Thomas also would be sidelined for at least a few weeks.
Receiver Cooper Kupp handled returns after Cooper was sidelined and could fill the role going forward, but McVay said all options would be explored.
"Whether we handle that internally or we go outside of somebody else to figure that role out, those are things that we've kind of been discussing," McVay said. "In terms of making that final decision that will probably be something that we'll probably decide on in the next day or so."
Cooper, a third-year pro, returned two punts for 12 yards and returned three kickoffs for 75 yards against the Raiders.
Last season Cooper was named to the Pro Bowl after averaging 12.5 yards per punt return and 27.4 yards per kickoff return.
The Rams play the Arizona Cardinals on Sunday at the Coliseum.