The Fire Department of New York confirmed the fatality and is on the scene responding to the accident.
The collapse happened along Broadway early on Friday morning in the Tribeca neighbourhood.
The downed crane, which filled the street, fell onto numerous parked cars.
"It was right outside my window," witness Robert Harold told the AP news agency. "It was a crashing sound. You could feel the vibration in the building. I looked out the window and saw it lying in the street."
Mr Harold said he saw someone trapped in a car and someone lying in the street.
Emergency responders are on the scene and Mayor Bill de Blasio is on his way.
The weather in New York City this morning was windy with snow flurries.
It is not yet known exactly why the crane collapsed, but photos show that the base of the crane flipped over.
Public transportation is delayed and subway trains are bypassing the area due to the collapsed crane.
Police officers in the area told people arriving for work they should go back home.
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