Emergency services were called Kellaway Crescent in Mill Park about 7.50pm in response to reports of a stabbing.
A woman, aged 39, was also pronounced dead at the scene.
Police said they found a man, the woman and the girl, who are believed to be known to each other, with critical injuries.
The young girl was taken to hospital in a critical condition, where she died.
Police said the man, 40, who is under police guard in hospital, is also in a critical condition.
Anyone with information should call Crime Stoppers on 1800 333 000.