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. He is currently in a Wake County juvenile facility.
The girl was taken to Duke University Hospital with critical injuries. Her condition is unknown at this time.
According to police, the unidentified teens are related and lived in the same house where the shooting happened.
Investigators are still trying to determine the circumstances surrounding the shooting. Further details have not been released at this time.