Officers were called to a residence on Chicago Way just before 5:30 p.m.
The girl's father, who says he was not home at the time, says his daughter was likely shot by a stray bullet that came through the house.
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He says he was notified by his wife that their daughter was shot.
Police did not confirm the girl was shot, but said she was taken to the hospital with life-threatening injuries.
Anyone with information about the incident is asked to call the SFPD Tip line at 1-415-575-4444 or Text a Tip to TIP411 and begin the text message with SFPD. You may remain anonymous.