Burfict appeared to twist Panthers quarterback Cam Newton's ankle after he scored a touchdown during the third quarter. He also seemed to do the same move to tight end Greg Olsen after he scored a touchdown in the fourth quarter. Newton and Olsen have each battled ankle injuries this season.
Earlier this week, Olsen called for Burfict to be suspended.
"Punishment needs to go beyond a fine," Olsen said on Monday. "Guys like that don't learn from that stuff. He's been fined a hundred times for headhunting, and he did it to Kelvin [Benjamin] again. You watch the film; that's just what he is.
"At some point, if the NFL wants to really say they care about guys' safety, they've got to start putting guys out for weeks. Me and Cam are lucky we aren't out for weeks, or Kelvin isn't out for weeks. If you're going to start putting guys on other teams out, then the ramifications need to equal that."
Burfict, 24, led the Bengals with eight unnecessary roughness penalties last season and has been fined several times during his career. He sustained a concussion in each of the team's first two games this season and missed Week 3 and 5 before returning against the Panthers. He was selected to his first Pro Bowl last season.
Cincinnati and Carolina tied on Sunday after Bengals kicker Mike Nugent missed a field goal as overtime ended. The Bengals are 3-1-1 and play the Indianapolis Colts on the road in Week 7. The Panthers are 3-2-1 and play the Green Bay Packers on the road on Sunday.