Authorities in Mississippi said the child grabbed the gun when he wanted the controller and his sister did not hand it to him.
The girl, named in media reports as Dijonae White, was rushed to hospital after the bullet entered her brain.
Monroe County Sheriff Cecil Cantrell told local media the girl later died.
Local media reported that neighbours were shocked by the incident, while a family member described Dijonae as a “great girl”.
On Facebook members of the community voiced concerns about the availability of guns and the presence of video games, while others simply offered prayers for the girl and her family.
It is not known how the child was able to access the gun, authorities said, but the circumstances of the incident are being investigated.
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The children’s mother is believed to have been feeding other children when the shooting took place, it was reported.
Sheriff Cecil Cantrell told WTVA that he was unsure what consequences the boy would face, adding he was unaware of a case where a child had shot another in a similar manner.