Kamilah Peniston, from the Gorton area of Manchester, was taken to Manchester Royal Infirmary on Monday evening suffering gunshot wounds.
She was later transferred to Pendlebury children's hospital, where she died the following morning.
Greater Manchester Police recovered a handgun converted to fire live ammunition at the address on Wembley Road, Gorton, where the shooting took place.
Detective Superintendent Ian Foster, who is leading the investigation, said the events leading to her death were "tragic".
The teenager is due to appear before Manchester City magistrates court today.
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