The plane went off the runway and into a grassy area after making the emergency landing around 9 p.m. Wednesday.
Airline spokeswoman Leslie Scott says Delta Flight 886 was carrying 118 passengers. No one was injured.
Scott says the plane was diverted to JFK because it has longer runways. She says the McDonald Douglas MD88 was taxiing to the terminal when it rolled onto a grassy area.
Passengers were taken to Terminal 2, where buses to LaGuardia were provided.
The FAA is investigating.