New York police and fire crews were on the scene, and part of the street had been closed off as a precaution, the New York Police Department said.
Authorities have asked all occupants of upper floors in buildings near the site of the collapse to evacuate to lower floors.
The evacuation zone expanded later, covering all buildings north and south of 57th Street, between Sixth and Seventh avenues, in addition to buildings on 56th Street, New York Fire Department spokesman Michael Parrella said.
One57, the skyscraper under construction, is offering some of the most expensive apartments in New York, with a penthouse there recently closing for a whopping USD 90 million, according to The New York Times.
"At approximately 2:35 p.M. Today, the One57 tower crane boom became damaged by the high winds of Hurricane Sandy," according to Mary Costello, senior vice president for Lend Lease, the property group managing the site.
"The hurricane storm winds have pushed the crane boom over the cab section of the high-rise crane at One 57th Street," CNN quoted Costello as saying.
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"We are working with structural engineers and the DOB (New York City's Department of Buildings) on evaluating any additional measures that can be taken to secure the boom and crane structure. Current weather and wind conditions remain very severe," she added.
The Department of Buildings on Sunday issued guidance that all cranes needed to be secured ahead of the brunt of superstorm Sandy. It was not immediately clear whether that guidance was followed at One57, CNN reported.
Costello said the crane was last inspected on Friday.
Upon completion in 2013, the 90-storey One57 structure will stand at 306 meters tall, making it one of the tallest buildings in the city.