Amateur video shows the helicopter crashing into the water, its rotor still spinning, and then overturn.
The person who escaped was scooped up by a tug boat, sources said.
The crash happened near the mayoral residence.
"The pilot freed himself, the other five did not", Fire Commissioner Daniel Nigro told reporters during a brief press conference. "By the time we got out here, we couldn't see it".
The Federal Aviation Administration said the Eurocopter AS350 went down near the northern end of Roosevelt Island at about 7 p.m. and was investigating.
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The skies over NY constantly buzz with helicopters carrying tourists, businesspeople, traffic reporters, medical teams and others.
The other three were taken to hospital in critical condition.
The NYC Ferry said late Sunday on Twitter that service on the Astoria and East River routes was now suspended until further notice because of the helicopter crash.
The NYPD and FDNY confirmed rescue operations are under way. In June 2005, two helicopters crashed into the East River in the same week. The other hit the water shortly after takeoff on a sightseeing flight, injuring six tourists and the pilot.
It was not immediately clear what caused the crash and the extent of possible injuries.