A photo of Ryan's rejoinder to boisterous Dolphin fans was captured by a cell phone camera and forwarded to Jorge Sedano of 790 The Ticket, an ESPN Radio affiliate in Miami.
"It was stupid and inappropriate," Ryan said in a statement released by the club. "I wouldn't accept that type of behavior from one of the coaches or players and its unacceptable from me. I apologize to the Jets organization, the National Football League and NFL fans everywhere."
Jets general manager Mike Tannenbaum also released a comment.
"Rex showed extremely poor judgment, and his conduct was inappropriate," Tannenbaum said. "He knows he was wrong, has apologized and we have accepted his apology. Any other actions regarding this incident will be addressed internally by the organization."
The MMA event featured former NFL running back Herschel Walker making his debut and was televised by Showtime.
Ryan elicited loud boos from the crowd when a ringside Showtime interview was shown on the Bank Atlantic Center video scoreboard.
"I'd like to thank everybody here in Miami. I know they love me," Ryan said with a grin.
"I want to just tell everybody in Miami, hey, we're coming to beat you twice next year."
Ryan led the Jets to the AFC Championship Game after they went 9-7 during the season to earn a wild card in his first year as an NFL head coach. He made headlines with his confident statements, including saying the Jets should be the favorite to win the Super Bowl when the playoffs began.
He previously had a verbal feud with Miami linebacker Channing Crowder, and deep in Dolphins territory, he was a likely target for boos.
At the Pro Bowl in Miami, several of the Jets' Pro Bowl players supported their coach.
"He's one of those guys who if you come at me, I'm coming at you. It was all in fun. They were probably yelling and talking stuff at him and it ticked him off. Fans can be like that," defensive end Shaun Ellis said, according to the New York Post.
Cornerback Darrelle Revis said he thought Ryan took the right approach in apologizing.
"The only thing I've got to say about that is we're human, coaches and players, we're human and we have feelings," Revis said, according to the New York Post. "We get angry just like the next person. I wouldn't say it was the right thing to do, but he apologized and that was the right thing to do -- apologize and move forward."
Guard Alan Faneca wasn't surprised by Ryan's response to the hecklers.
"Man, I love Rex," Faneca said, according to the New York Post. "Rex can be who he is and it doesn't matter to me. ... That's the face that [Jets owner] Woody [Johnson] chose, so that's the face we go with."
Ryan could be subject to a league fine under the NFL's personal conduct policy.
ESPN.com's Tim Graham and The Associated Press contributed to this report.