"Nobody knew what was going on," Beth Henderson, 24, of Brooklyn, New York, told ABC News. "There was a gnawing worry in the pit of my stomach."
The jet, with 200 passengers and nine crew members on board, was taken to a secure area at JFK after landing and a bomb squad, K-9 units and emergency services were dispatched, according to the Fire Department of New York.
Passengers got off the plane and were taken to "holding buses," Robert Wolf, a passenger on the flight, tweeted.
The plane was evacuated and there were no reports of injuries.
Police used bomb-sniffing dogs to check passengers' luggage. Four dogs inspected each piece of luggage on the flight.
No explosives were found and the airport was cleared, the FBI told ABC News.
It is unclear who made the threat and how it was made.
"AA airlines apologizes to [its customers] for any inconvenience this may cause however the safety of the passengers and crew is our top priority," the airlines said in a statement issued Sunday.