The team announced Kirkpatrick, 27, would not return to action, while fellow cornerback Adam Jones was also ruled out.
He had one tackle before coming out of the game.
In his sixth NFL season, Kirkpatrick matched a career high in interceptions in 2016. He's posted 12 tackles with zero interceptions through the Bengals' first four games.
"The frustration for me is very high right now," Kirkpatrick told reporters in the midst of the Bengals 6-9-1 season in 2016, "because at the end of the day, I don't care about no interceptions, none of that. The only thing I care about is getting W's and winning. I've been winning ever since I started playing this game. So we ain't getting them, for me, that's heartbreaking."
Kirkpatrick previously missed a Week 4 matchup with the Miami Dolphins last season due to a calf injury. Josh Shaw and Darqueze Dennard will get additional snaps if Kirkpatrick is out for an extended time.