Garrett will miss at least the rest of the season, including any potential playoff games, for swinging Mason Rudolph's helmet at the quarterback in the final seconds of the game.
The 2017 No. 1 pick will be required to meet with commissioner Roger Goodell "prior to a decision on his reinstatement."
"Last night, I made a terrible mistake. I lost my cool and what I did was selfish and unacceptable," said Garrett in a statement. "I know that we are all responsible for our actions and I can only prove my true character through my actions moving forward.
"I want to apologize to Mason Rudolph, my teammates, our entire organization, our fans and to the NFL. I know I have to be accountable for what happened, learn from my mistake and I fully intend to do so."
Steelers center Maurkice Pouncey received a three-game ban for kicking and punching a downed Garrett, while Browns defensive end Larry Ogunjobi was given a one-game suspension for shoving Rudolph to the ground.
Additionally, the Steelers and Browns have each been fined $250,000.
Garrett is expected to appeal his suspension, a league source told Nate Ulrich of the Akron Beacon Journal.
Pouncey is also expected to challenge his ban, a source told Ian Rapoport of NFL Network.
The league added that "additional discipline for other players with be forthcoming."
"We are extremely disappointed in what transpired last evening at the end of our game. There is no place for that in football and that is not reflective of the core values we strive for as an organization," said Browns owners Jimmy and Dee Haslam in a statement. "We sincerely apologize to Mason Rudolph and the Pittsburgh Steelers.
"Myles Garrett has been a good teammate and member of our organization and community for the last three years, but his actions last night were completely unacceptable. We understand the consequences from the league for his actions."
Garrett was in the midst of a stellar campaign, racking up 10 sacks and two forced fumbles to put himself firmly in the conversation for Defensive Player of the Year in his third NFL season.
The Browns and Steelers are set to play again in Week 13.