A National Football League spokesman said the NFL is investigating the incident, the New York Daily News reported.
On the video, Ryan can be heard and seen shouting "shut the (expletive) up." The exchange occurred at halftime as the Jets were in the midst of losing 37-16 to the New England Patriots.
"Hey, Rex, Belichick is better than you," the fan yelled, referring to Patriots' coach Bill Belichick.
By Monday, Ryan had cooled down.
"It was an emotional time coming in," he said. "I obviously made a mistake. I was full of emotion and just popped off. Obviously I know I represent the National Football League. I know I represent the Jets. And I know it was a mistake. I apologize for it. This is who I am. I made a mistake. I'm about as big a competitor as there is."
The Jets fined Ryan $50,000 for an obscene gesture to a heckler during a mixed martial arts competition in Miami in 2010. The team said any penalty for Sunday's incident is in the hands of the NFL since the coach lost it during a game.