Kolb practiced last week, but said he didn't feel fully recovered. He was listed as questionable. He suffered the concussion during a 21-19 win over San Francisco on Dec. 11.
Skelton made his sixth start of the season. He also took over for four games earlier in the season when Kolb had an injured foot. Skelton nearly rallied the Cardinals, but the Bengals held on to win 23-16 and officially end Arizona's playoff chances.
Bengals receiver Andre Caldwell was inactive for the second straight game with a groin injury.
Cincinnati got right tackle Andre Smith back. He'd missed the last two games with an ankle injury. Receiver A.J. Green was in the starting lineup despite being limited in practice last week with a sprained right shoulder.
Information from The Associated Press contributed to this report.