The 28-year-old Clemens joined the Texans (9-3) on Nov. 23 after quarterback Matt Schaub was injured and needed season-ending surgery to repair a Lisfranc injury in his right foot. Backup Matt Leinart was injured in the next game, rookie T.J. Yates became the starter and Houston signed Jake Delhomme to back up Yates.
Yates completed 12 of 25 passes for 188 yards and a touchdown in the Texans' 17-10 win over Atlanta on Sunday. Hartmann, an undrafted rookie out of Central Michigan, tore his left anterior cruciate ligament late in the game.
Coach Gary Kubiak said Monday that Houston would sign another punter after holding tryouts. Houston plays at Cincinnati (7-5) on Sunday.
Information from The Associated Press contributed to this report.