Panthers tight end Greg Olsen called it a "premeditated attack" and said Burfict should be suspended.
Olsen also accused the linebacker of intentionally targeting players who recently came back from ankle injuries.
Carolina place-kicker Graham Gano was vocal on Twitter about the allegations, saying: "unbelievable that a player would intentionally try to hurt my teamates twice. I hope the NFL lays down the law hard. Unacceptable."
ESPN says Burfict led the Bengals in penalties last season, including eight for unnecessary roughness.
He was flagged for two personal fouls in Sunday's game unrelated to the alleged ankle twisting.