Webster had played just two snaps in his season debut against the Dallas Cowboys on Sunday before exiting with a quad injury. He had been out since last December with a torn Achilles sustained as a member of the Los Angeles Rams.
The Texans already have cornerbacks Kevin Johnson (concussion) and Jermaine Kelly Jr. (undisclosed) on injured reserve. Aaron Colvin missed the Sunday game with an ankle injury and is out indefinitely.
(With inputs from agencies.)