Webster, who was playing in his first game since he tore his Achilles with the Rams last December, left the Texans' Week 5 victory over the Cowboys with a quad injury. He played just two snaps before the injury.
Houston has already placed cornerback Kevin Johnson (concussion) on injured reserve and will be without cornerback Aaron Colvin (ankle) indefinitely. The Texans relied heavily on Shareece Wright after Webster's injury and have used safety Kareem Jackson in both roles as well.
On Monday, coach Bill O'Brien said he'd "really like to try to keep [Jackson] at safety" because of how well he has played there this season, but acknowledged using the veteran at cornerback is a possibility. Jackson played corner before making the switch to safety this offseason.
The Texans also signed safety Mike Tyson to the active roster from the practice squad and added cornerback Robert Jackson to the practice squad.