The Giants will be without a key piece of their defense for at least four weeks.
Big Blue placed Kayvon Thibodeau on injured reserve on Saturday after suffering a wrist injury in last week's game against the Seahawks.
Thibodeau underwent surgery earlier this week with a fractured navicular bone in his wrist, NFL Network reported.
The surgery was not expected to be season-ending.
Head coach Brian Daboll told reporters Wednesday that Thibodeau is expected to play every week.
Thibodeau, 23, had 12 tackles and two sacks in the Giants' first five games.
In addition to outside linebacker, the Giants also have running back Devin Singletary (groin), punter Jamie Gillan (hamstring) and wide receiver Bryce Ford-Wheaton (shoulder) on Sunday night against the Bengals. He will be absent.
Receiver Isaiah Hodgins and running back Dante Miller have been removed from the practice squad and will be active against Cincinnati.
With Gillan sidelined, New York signed punter Matt Haak and added him to the active roster.
