Foster didn't practice all week after injuring his back on Houston's first series against Indianapolis last Sunday. He also missed most of Houston's previous game with a hamstring problem.
Interim coach Wade Phillips said Friday that Foster had visited specialists about the problem. The Pro Bowl player gained 542 yards on 121 carries with one touchdown and had 22 receptions and another score.
Ben Tate, still recovering from four broken ribs, is expected to start Sunday at Arizona. Dennis Johnson and Deji Karim, who were both signed last week, will play behind Tate.
It's been a difficult season for the Texans, who previously lost star linebacker Brian Cushing to a knee injury for the second straight year. Coach Gary Kubiak suffered a mini-stroke during last week's loss at Indianapolis, and his coaching future is uncertain. The team has said Kubiak is expected to make a full recovery.
The Texans entered Sunday's game against the Cardinals at 2-6 after winning the AFC South the last two seasons and posting a playoff victory each year. Foster was a key to the franchise's first two post-season appearances.
He has rushed for at least 1,200 yards in each of the last three seasons, including leading the NFL with 1,616 yards and 16 touchdowns in 2010. He also had 15 TDs rushing, tops in the NFL, in 2012.
Foster was an undrafted free agent out of Tennessee who won the starting job in his second pro season.
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