In a hard landing, a plane touches down with excessive vertical speed or force, exceeding the manufacturer limit.
The FAA said on social media that air traffic control "was not providing services to the aircraft" at the time of the incident.
The New York Times reported that the plane was coming from the Hamptons - a seaside retreat for affluent New Yorkers - and was heading to a seaplane base when it struck a wave while landing, leading to it partially capsizing.
Another seaplane was damaged in the East River three weeks ago. That aircraft, a small two-seater, was struck by a large wave as it tried to take off from the river on 13 June.
During that earlier incident, the FDNY took a pilot and one passenger on to a boat after the plane went down near Queens, CBS News reported.
