Foster was limited in practice all week and was declared inactive by Houston.
Rookie Alfred Blue will start in Foster's place.
In the Texans' first two games of the season, Foster gained 241 yards on a league-high 55 carries. Since 2010, when Foster became the Texans' starter, he leads the NFL in carries per game with 20.97.
Foster, who turned 28 in August, missed eight games last season with a back injury. He had previously struggled with hamstring and calf injuries before the 2013 season began. Foster had back surgery in November.
The Texans drafted Blue out of LSU in the sixth round this May.