Dozens of panicked tourists were sent running for cover after the gunman - who survived and was later reported as being in a critical condition in hospital - started shooting on the 86th floor of the New York City landmark.
David Robinson, a British tourist, said:"I'd been out there about one minute when I heard what I thought to be firecrackers. Then everyone started panicking."
Seven people were injured after the shooting, including some who were trampled when visitors scrambled towards the exits and lifts in a bid to escape.
A police spokesman said the dead person was the intended target. Two of those wounded were French and in a serious condition. One victim was thought to be a child. A one-block area surrounding the Empire State Building in Manhattan was blocked off as dozens of ambulances from area hospitals, police and fire trucks converged on the area.
The Empire State Building, which opened in 1931, is one of New York City's top tourist attractions, and at 1,250 feet high it ranked for years as the world's tallest building. It has been featured in hundreds of movies, including the climactic scene of the film classic King Kong in which the ape clung to its side as he battled a squadron of attacking planes.