The victim, a male resident, died at the hospital and has not yet been identified, they said.
US President Donald Trump has a home and an office in the building, but is currently in Washington.
The fire was reported to be on the 50th floor of the high-rise, which contains apartments and office space.
The president tweeted that the fire was out, and had been "very confined" as the tower is a "well-built building".
Streets surrounding the building in Midtown Manhattan have been closed off.