The fire department initially had said that the worker fell onto the bridge's midspan.
The subcontractor was at the base of the Queens tower installing fencing when he fell.
On Thursday, a construction worker fell to his death in Brooklyn. He lost his balance and fell about 50 feet.
Police said 35-year-old Louis Zaruma, of Brooklyn, was putting up steel framework for the 6th floor of a residential building when he fell.