Local media reported the family were visiting a relative in Chakwal, in the Punjab province, when they were robbed while in their rental car on Wednesday night (local time).
Two robbers on a motorcycle, including one with a pistol, fled when they were spotted by an officer, and the rental car also drove off.
"As the cops saw the vehicle being driven away immediately, they took it as belonging to the robbers and opened indiscriminate fire on the car," a police official told local media.
The family from the Perth suburb of Kewdale was rushed to hospital, where the girl was pronounced dead.
Her father and older brother were seriously injured, while her mother was unharmed.
The Department of Foreign Affairs and Trade confirmed it was providing consular assistance to the family of an Australian who was killed and to two Australians who were injured.
"We send our deepest condolences to the family at this difficult time," a department spokesperson said in a statement.
Pakistani Association of Western Australia general secretary Asim Chaudhry said the incident had left the local community downcast.
"This news is very shocking, especially the death of the nine-year-old," he told Nine News.
"They just came from the pilgrimage (to Mecca)."
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