Ryan was walking into the tunnel for halftime when a fan told Ryan, "Hey, Rex, Belichick is better than you."
The Jets coach, whose team was down 13-9 at the time, responded with a curt, "Shut the f--- up."
New York ended up losing to the Patriots, 37-16, and followed that with a loss to the Denver Broncos on Thursday night. Tied for second in the AFC East at 5-5, New York's playoff hopes are in jeopardy.
Ryan has been fined before. The league forced Ryan to pay $50,000 in February 2010 after he was caught giving the middle finger to a fan during a UFC event in Florida.
The coach already apologized for his remarks last week.
"I obviously made a mistake," Ryan said last week. "I was full of emotion and just popped off. Obviously, I know I represent the NFL, I know I represent the Jets, and I know it was a mistake. I apologize for it. It's who I am sometimes ... I'm about as big a competitor there is. At that time, I was in no mood to hear anything, but I also understand I have to handle that better."