Foster aggravated the injury during the Texans' Sunday night game against the Indianapolis Colts. He played only the first series of Houston's 27-24 loss.
Foster was limited in practices last week by a hamstring injury that prevented him from finishing the Texans' Oct. 20 loss to the Kansas City Chiefs.
The running back has had injuries to his back, hamstring and calf since the start of training camp. He began camp on the physically unable to perform list because of the calf injury. After his calf healed, he suffered a back injury that he said was not related and remained on PUP.
If they're without Foster on Sunday against the Arizona Cardinals, the Texans will start Ben Tate, who played most of the game against Kansas City despite four broken ribs and who played all of the game against the Colts despite his injury not having healed completely.
Phillips said Tate was sore but that he'd be ready to play against the Cardinals.