Hampton (7-10, 5.30 ERA) went on the 15-day disabled list on Tuesday. He left his last start on Aug. 13 with shoulder soreness. An MRI taken Wednesday revealed the extent of the injury, the team announced.
The Astros said Hampton will not have surgery to repair the injury.
The 36-year-old has started 21 games this season, his most since 2004. He missed the 2006 and 2007 seasons after separate elbow surgeries.
Yorman Bazardo (0-0) started in Hampton's place in Wednesday night's game against Florida.