Kitna went down when hit by two Cardinals defenders as he threw an incomplete pass out of a shotgun on fourth-and-2 from Arizona's 38 with 7:22 to play in the first half. A defensive-offside penalty gave Dallas a first down.
Kitna said after the game that he had a "strained left oblique."
"We tried to do what we could to block the pain," he added. "We were hoping it was a hip pointer, but it's more than that."
Kitna was uncertain if he would be able to play in Dallas' season finale at Philadelphia.
The 38-year-old quarterback's game got off to a shaky start when Arizona intercepted two of his passes in the first quarter, returning both for touchdowns. Kitna was sacked three times before he left the game.
The Associated Press contributed to this report.