Burfict did not practice all week after suffering a hip injury that sidelined him in the second half of last week's 45-10 loss at Kansas City.
Also ruled out for Cincinnati on Friday was wide receiver John Ross, running back Giovanni Bernard, cornerback Darqueze Dennard, tight end Tyler Kroft and linebacker Nick Vigil. In addition, rookie center Billy Price was listed as doubtful.
Burfict has struggled since returning to the lineup after serving a four-game suspension for performance-enhancing drugs. He had a career-high four missed tackles in the loss at Kansas City.
Bengals coach Marvin Lewis acknowledged that Burfict has not played up to his previous standards. In addition, Burfict was fined $112,000 by the NFL for two unnecessary calls against Pittsburgh in Week 6.
Burfict, in his seventh season out of Arizona State, is the most fined player in the NFL, paying $415,637. He has now been fined 11 times. He has also been suspended six games, including a three-game ban after an illegal hit on Brown in a 2016 playoff game.
Ross is expected to be sidelined a few weeks with a groin injury. He aggravated the injury during Sunday's loss. The ninth overall pick of the 2017 NFL Draft, Ross missed two games with the groin injury before returning for Sunday's game.
The 22-year-old Ross has recorded seven receptions for 79 yards and two touchdowns this season.