Per NFL Network's Tom Pelissero, the NFL docked Garrett a total of $42,112 for his infractions during Monday's 23-3 win.
Garrett was flagged twice in the first half for roughing the passer. The second one came in the second quarter and resulted in Siemian suffering a season-ending ankle injury that will require surgery.
The Browns star was flagged for a total of four penalties and addressed questions about being a dirty player this week.
"I know who I am and the guys within these walls know who I am, and that's not me," he said, via Cleveland.com's Mary Kay Cabot. "I'm not going to do anything to try and hurt this team or take out any player outside the rule book. I'm just going to keep playing this game the way it's supposed to be played and that's violently but passionately."
New York turned to third-string quarterback Luke Falk to finish the game.
Regardless of who was playing quarterback for the Jets, Garrett was a constant fixture in the backfield in Week 2. The 2017 No. 1 overall pick recorded five quarterback hits and three sacks when he wasn't getting called for penalties.