The person suffered a heart attack when he was preparing a tank on the set and someone noticed that there was no bubble surfacing from the gear, reported TMZ online.
The man was later admitted to a nearby hospital via helicopter, but EMT (Emergency medical technicians) were unable to restart his heart on the flight.
He was eventually pronounced dead at the hospital.
Law enforcement forces said that the cause of the dead appeared to be "a heart attack," and investigators were treating the case as "a natural death." An autopsy for the man is expected to be completed over the weekend.
The filming of Gore Verbinski's Western film was postponed following the incident.
"We regretfully confirm that a 'Lone Ranger' crew member has passed away after being taken to a local hospital. Our full support is behind the investigation into the circumstances of this terrible event," a representative of Disney Pictures said in a statement.
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"The Lone Ranger" will reunite Depp with Verbinski, who helmed the "Pirates of the Caribbean" film series. The film also stars William Fichtner, Ruth Wilson, James Badge Dal and Tom Wilkinson.
The film will be released in the US on July 3, 2013.