It happened around 6 p.m. Thursday in the 1900 block of Faucette Avenue.
When officers arrived, they arrested a 15-year-old boy and charged him with assault with a deadly weapon with intent to kill inflicting serious injury. Authorities said those charges will be upgraded after the girl's death.
The boy is currently in a Wake County juvenile facility.
The girl, later identified as Emily Lopez, was taken to Duke University Hospital with critical injuries. She died early Monday morning at the hospital.
According to police, Lopez and the unidentified 15 year old were related and lived in the same house where the shooting happened.
Investigators are still trying to determine the circumstances surrounding the shooting.