The plane's four occupants swam to shore.
It happened about 200 yards from the beach near Jessup Neck around 1:30 p.m.
FAA says the plane, a Cessna Caravan sea plane, intentionally landed in the water, but hit a large rock in the water.
That caused the plane to tilt to one side, damaging one wing.
Four people swam to the beach, where they awaited rescue.
The plane was en route to East Hampton Airport when the pilot realized the small aircraft would not make it, officials said.
North Sea is a hamlet on the South Fork of Suffolk County. It is located in the Town of Southampton.
The plane is operated by V1 Jet Management LLC of New York.