Australian-born Hania Ahmed and her family were visiting a relative at Chakwal, in Pakistan's Punjab province, when they were robbed while in their rental car late on Wednesday night (local time).
In a lengthy statement posted to X on Monday morning (Australian time), Punjab Police confirmed Crime Control Department officers intervened after the Perth family was taken hostage at gunpoint.
The suspects fired at a police officer, leading to an exchange of gunfire.
"In the ensuing chaos, the officer involved mistakenly assessed that the suspects were attempting to flee in the victims' vehicle and discharged his weapon," the statement said.
"This erroneous decision resulted in the tragic death of ... Hania and injuries to her father and brother."
The girl's mother was unharmed in the shooting.
Prime Minister Anthony Albanese said the incident needed to be properly examined by authorities.
"These circumstances do need to be examined. They need to be examined in a transparent way, so that everyone can know, the family, most importantly, but others as well," he told reporters in Canberra on Monday.
"Australia expects there to be transparency and a proper investigation of these circumstances.
"My heart goes out to the family and friends, and indeed the Pakistani Australian community will be really feeling this today. A nine-year-old girl visiting Pakistan with her family should have been a time of joy."
The officer who opened fire on the Australian family's car completely deviated from established standard operating procedures and legal principles governing the use of force, police said.
He has been suspended from duty, formally arrested and faced court, where he was remanded to judicial custody in jail.
His weapon and spent shell casings are among the forensic evidence collected and sent for processing.
Pakistani police have promised a "thorough, impartial investigation to ensure that justice is served".
"We recognise that our primary duty is the protection of human life, and any failure to adhere to the principle of 'minimum force' is treated with the highest level of legal and departmental accountability," local police said.
"We are deeply saddened by this tragedy.
"While our personnel operate in high-risk environments, there is no justification for a departure from our protocols."
Hania was in grade 4 at Australian Islamic College at Kewdale in Perth's east.
The school, where her older brother attends grade 5, held a special assembly with students on Friday afternoon and has offered counselling services.
Executive principal Abdullah Khan remembered Hania as a "happy, bubbly, friendly girl".
"She had lots of friends, was very social and was liked by peers and teachers," he told AAP.
Mr Khan said he spoke with Hania's father, Adeel, on Sunday and communicated the school and community would wrap their arms around the family upon their return.
"He is devastated," he said.
"He's recovered well but the brother is still hospitalised and going through the treatment."
