Schaub was hit low in the third quarter and was booed by Texans fans while leaving the field.
Backup quarterback T.J. Yates has entered the game to replace him.
Schaub has taken heavy criticism lately for his high interception rate. He was second in the NFL with nine picks heading into this game and set an NFL record last week after throwing a pick-six in four consecutive games.
Houston fans have been calling for the quarterback's benching this week, and head coach Gary Kubiak mulled the option of starting Yates against the Rams.
Schaub was 15-for-21 with 186 yards and no interceptions at the time of the injury. His team trailed 31-6, however, and look to be on their way to a fourth consecutive loss after opening the season 2-0.
T.J. Yates threw a pick-six himself after taking over.