Bradford hasn't been able to practice this week because of a high ankle sprain. He was hurt near the end of last week's loss at Green Bay.
He had been listed as questionable and was said to be a game-time decision.
The Rams signed quarterback Tom Brandstater to their 53-man roster off their practice squad after it was decided Bradford wouldn't play.
The Rams also waived receiver Nick Miller.
Information from ESPN.com senior NFL writer John Clayton, ESPN senior NFL analyst Chris Mortensen and The Associated Press was used in this report.