The National Football League fined the Pittsburgh Steelers and Cleveland Browns $250,000 each and suspended three players involved in a violent incident at the end of a game between the two teams on Thursday night.

Thursday's incident occurred late in the fourth quarter when Browns' defensive end Myles Garrett tackled Pittsburgh quarterback Mason Rudolph shortly after he threw a pass to running back Trey Edmunds. The two players exchanged words and a slight skirmish led to Garrett ripping off Rudolph's helmet and hitting him in the head with it.

The incident escalated as players from both teams became involved, leading to the ejection of Garrett, Browns defensive lineman Larry Ogunjobi and Steelers center Maurkice Pouncey. Speaking to reporters after the game, Rudolph said he was OK but called Garrett's decision to use the helmet in the scuffle "cowardly" and "bush league."

A league source told CNBC all three players plan to appeal the suspension. Pittsburgh officials are hoping to get Maurkice Pouncey back by the Dec. 1 rematch against the Browns.

Three of the players — Garrett, Ogunjobi and Pouncey — have been suspended and fined. Garrett has been suspended without pay "indefinitely," the league said in a statement released on Twitter.

Pouncey has been suspended without pay for three games while Ogunjobi has to sit out one game without pay.

Garrett took responsibility for his part in the incident, saying he allowed emotions to overtake him leading to his "foolish" and "out of character" behavior.

"I made a mistake," he told reporters. "I lost my cool, and I regret it. It's going to come back to hurt our team."

He released a statement on Friday apologizing to Rudolph, his teammates, the NFL and fans. "I know I have to be accountable for what happened, learn from my mistake and I fully intend to do so," he said in a statement released by the team on Twitter.