Riverhead police say it happened Wednesday afternoon at Calverton's Skydive Long Island company, which says it offers the highest jumps on Long Island at 13,500 feet.
Police say one man was pronounced dead at the scene. The other man was airlifted to a hospital in critical condition. The Federal Aviation Administration is investigating the accident.
A New York City Department of Correction spokesman says the man who died was a correction officer.
Skydive Long Island says it owns million-dollar aircraft and a 23,000-square-foot hangar on 16.3 acres of land. A message left with the skydiving company hasn't been returned.
The identities of the victims haven't been released.
No other information has been provided by police.