Merseyside Police said officers received a report at 3.50pm on Monday that a child had been attacked by a dog at an address on Bidston Avenue, Blackbrook.
Emergency services attended and the child was taken to hospital where she died of her injuries.
The dog was handed over to police at the address and has been humanely destroyed.
Police said the animal will be subject to further forensic examinations to determine its breed and whether it is, or is not a legal breed under the Dangerous Dogs Act (1991).
Detective inspector Lisa Milligan said the dog had only been with the family for a week.
She said: “This is a tragic incident and our thoughts are with the child’s family at this devastating time. The little girl’s parents and wider family are absolutely devastated and our specialist Family Liaison Officers are providing them with support at this horrendous time.
“Whilst we are in the very early stages of the investigation into this extremely tragic incident we can confirm that the dog was only bought by the family a week ago and officers are working to identify the previous owners of the dog concerned and establish its history.
“Our officers will remain on Bidston Avenue this evening and in the coming days to provide reassurance to the local community and we will work tirelessly to establish the full circumstances.
“If you were in the Bidston Avenue area this afternoon and witnessed anything, or have any information about the dog then please come forward speak to one of our officers.