Talib will undergo ankle surgery Thursday after he suffered a high-ankle sprain in a victory over the Los Angeles Chargers.
"It's unfortunate," Rams coach Sean McVay said about Talib's injury earlier this week.
McVay was unable to provide a specific timeline for Talib's return, but the 11th-year pro will be sidelined for at least eight weeks on injured reserve.
Cornerback Marcus Peters is questionable to play Thursday after he suffered a calf strain against the Chargers. McVay said Peters would be a game-time decision.
The Rams also promoted cornerback Dominique Hatfield to the active roster from the practice squad.
The Rams acquired Talib in March from the Denver Broncos in exchange for a fifth-round pick. He is scheduled to earn $19 million before his contract expires after next season.
With the Rams, Talib was reunited with defensive coordinator Wade Phillips, whose defense he starred in during the Broncos' 2015 Super Bowl season.
His leadership and knowledge of the defense enabled him to quickly become a cornerstone of the Rams' locker room and he was voted to captain by teammates. Talib, a five-time Pro Bowl selection, has seven tackles and two pass deflections this season.
The Rams are 3-0 as they prepare to play the Minnesota Vikings (1-1-1) on Thursday night at the L.A. Memorial Coliseum.