In a statement, the Mohave County Sheriff’s Office said the 39-year-old was hit in the head by a stray bullet as the Israeli-made Uzi kicked back. He was airlifted to the University Medical Centre in Las Vegas, where he was later pronounced dead.
A video released by the police showed the slender girl with a ponytail and wearing pink shorts being instructed in how to aim the gun by Vacca.
His final words, captured on video, were: “All right, full auto."
The nine-year-old had been at the range with her parents – the family were on holiday in the area.
Sam Scarmardo, the manager of the Last Stop range, told NBC News that "the establish[ed] practice at most shooting ranges is eight-years-old and up with parental supervision."
Friends of the dead man, a former soldier who was married with a young family, paid tribute to him on Facebook.
His best friend Robert Vera said: “He became a brother and a major part of my life through thick and thin. Rest In Peace brother.”
Describing Vacca as a "great guy, with a great sense of humour," Mr Scarmardo said he was "very conscientious and very professional."
"I just ask everybody to pray for Charlie, and pray for the client. She’s going to have a hard time," he added.
A popular tourist spot as the last place travellers can get food and fuel on their way to or from Las Vegas and the Grand Canyon, the Last Stop's website invites visitors to “Shoot a machine gun at Arizona’s last stop”.
According to the range’s website, visitors can take part in a “Burgers and Bullets” day, including lunch and a choice of more than 20 automatic weapons to shoot with.
It is illegal for children under the age of 18 to carry a gun in Arizona, but the rule does not apply on private property or if the youngster is accompanied by a parent or certified instructor.
The shooting is likely to lead to further calls for gun control in the US, an increasinlgy polarising topic across the country.
Ronald Scott, a Phoenix-based firearms safety expert, told AP: "You can't give a nine-year-old an Uzi and expect her to control it."