NFL.com's Ian Rapoport first reported the news.
Foster, who has also battled hamstring injuries this season, was sidelined by a strained calf for most of the offseason workouts. He didn't have a rushing attempt in last week's loss to the Colts, but was efficient in limited duty over the first six weeks of the season, averaging 19.5 carries and 88.5 yards per game in that time.
Ben Tate will now be the Texans' primary running back, after sharing the duty with Foster in recent seasons.
Rookie Dennis Johnson, who averaged 4.5 yards per carry against the Colts (8 carries, 36 yards), will serve as Tate's backup.
Foster, a former undrafted free agent, signed a five-year, $43.5 million contract extension with the Texans in March 2012.