Ryan, in South Florida for Sunday's Pro Bowl, attended a Mixed Martial Arts event the previous evening, where he was photographed making a one-fingered gesture.
"It was stupid and inappropriate," Ryan said in a statement.
"I wouldn't accept that type of behavior from one of the coaches or players and it's unacceptable from me. I apologize to the Jets organization, the National Football League and NFL fans everywhere."
The Dolphins fan who took the picture, David Hildenbrand, told the Miami Herald website he had shouted "Dolphins rule, Jets suck" at Ryan.
Jets general manager Mike Tannenbaum issued a statement on the team's website (www.newyorkjets.com) criticising Ryan.
"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."
(Reporting by Simon Evans; Editing by Patrick Johnston)