The Federal Aviation Administration said the plane was one of three that took off from Republic Airport in Farmingdale, New York, to celebrate Fleet Week – a US military celebration.
The remaining two aircraft returned safely to the airport.
In 2009, an airliner with 155 passengers and crew made an emergency landing in the river in what became known as the "Miracle on the Hudson".
Pilot Chesley Sullenberger was hailed a national hero after he steered the US Airways flight to safety after the plane struck a flock of geese.
