Claiborne was limited in practice on Thursday and Friday and officially listed as questionable for the game. He has passed all of the required tests, but he does not feel well enough to play.
The Cowboys will also use Sterling Moore, who was signed off New England's practice squad on Dec. 1, and Michael Coe, who was claimed off waivers from Miami last week, as their third and fourth cornerbacks.
Claiborne suffered the concussion in last Sunday's 20-19 win at Cincinnati in which he was hit by teammate Danny McCray while making a sideline tackle. He also suffered a gash on his lip that required 10 stitches to close.