A nine-year-old girl accidentally shot and killed a shooting range instructor in Arizona after the recoil on the Uzi submachine-gun she was learning to use sent the weapon over her head.

The instructor, Charles Vacca, 39, was standing next to the girl at an outdoor range when the accident happened on Monday, the Mohave County Sheriff's Office said.

"At about 10:00am, deputies responded to the Last Stop business located at 20606 North Highway 93 in White Hills. Investigations determined a nine-year-old girl accidentally shot the instructor in the head," the sheriff's office said in a statement.

The girl's family was visiting the shooting range while on holiday, the Los Angeles Times reported.

A video released by the sheriff's office shows Mr Vacca helping the girl with her stance and her grip on the gun before she fires a test shot.

"All right," Mr Vacca is heard saying.

The girl fires a few more shots and the weapon appears to tilt to the left before the video abruptly ends.

Mr Vacca was airlifted to a medical centre in Las Vegas, about 100 kilometres away, but died shortly after.

"This is a rarity for something like this to happen," a spokeswoman for the sheriff's office told the Los Angeles Times.