Bradford, who missed two games earlier in the season with a high left ankle sprain, aggravated the injury in a 23-20 loss to Arizona on Sunday. He practiced on a limited basis Wednesday, but the soreness increased.
"It went backwards a little bit, so in an effort to get it forward, we just kind of shut him down," Rams coach Steve Spagnuolo said.
Bradford, who has six touchdown passes and five interceptions for St. Louis, was limping noticeably Thursday.
Spagnuolo said a decision on Bradford's status for Sunday's game at San Francisco will be made Friday. Backup A.J. Feeley took the first-team reps on Thursday.
Long said he felt fine and sat out practice as a precautionary measure. He leads the team with 10 sacks.