A relative who was looking after the six-month-old child also suffered bite wounds as she tried to wrestle the animal off.
Police and paramedics were called to the address in Daventry, Northamptonshire, at 10.30pm on Friday night, where they tried to resuscitate the infant.
The six-month-old was taken to Northampton General Hospital where she was confirmed dead, Northamptonshire Police said.
The dog was destroyed at the scene.
Northamptonshire Police said they “cannot confirm the breed of dog” at this stage. But experts will carry out tests early next week to determine exactly what kind of dog it was.
Detective Sergeant Gary Baker, who is leading the investigation, said: “This was a deeply distressing and tragic incident and our thoughts are with the family who have been left devastated by the events of last night.
“Incidents such as these are extremely rare in this country, but that will be of little comfort to the relatives of this tragically young victim.
“The family have requested that they be left to grieve at this difficult time.”
Daventry Conservative MP Chris Heaton-Harris said the officers who went to the scene in Morning Star Road were left traumatised at the “horrific incident” they witnessed.
He said: “Obviously my thoughts and prayers are with the family. I would especially like to thank the officers who attended the scene last night.
“I understand they attempted to revive the baby girl and are badly affected by what they experienced.”
Mr Heaton-Harris was speaking after he had been briefed on the attack by the Northamptonshire Police and Crime Commissioner Adam Simmonds.
It is understood the force have dealt with 62 instances of attacks involving dogs in the past two years.