Williams suffered the injury when he was hit by linebacker D.J. Williams while reaching for a high pass during last week's loss at Denver. Miles Austin will replace Williams in the starting lineup.
Williams said Wednesday that he planned to play against the Chiefs, but he did not practice all week. Coach Wade Phillips said Friday that Williams' ribs hadn't healed well enough for him to play.
Williams and running back Felix Jones (knee) did not make the flight to Kansas City with the team. They have both been downgraded from doubtful to out, leaving the Cowboys without two of their top offensive weapons against the Chiefs (0-4).
Calvin Watkins and Tim McMahon are reporters for ESPNDallas.com.