The Rams had recently waived veteran Maurice Alexander in order to create a starting spot for rookie John Johnson. Now it'll be Blake Countess and Marqui Christian who will take Davis' place as the primary backups to Johnson and Lamarcus Joyner in the secondary.
The Rams also promoted defensive back Isaiah Johnson from their practice squad.
Davis, in his fifth year with the Rams, has an interception and three pass deflections this year, while acting as both a free safety and a strong safety.
Speaking from the team's practice facility Friday, Rams coach Sean McVay said he feels "good about the depth at safety" despite Davis' injury.
Davis will miss at least the next eight weeks and could technically be designated to return late in the season.
"Cody is a very important part of our team and it's unfortunate, but he had that quad that just wasn't getting any better," McVay said. "So, want to be smart, give him a full chance to recover, and then we'll look to bringing him back with the designated-to-return possibilities, the way that operates."