Ava Jayne Marie Corless was in bed at a house in Emily Street, Blackburn, at around 11pm yesterday when she was savaged by what police described as an American pitbull-type dog.
Police and ambulance staff attempted to resuscitate the girl but she was pronounced dead in hospital a short time later.
The girl's mother has been named locally as Chloe King and the man in custody, her current partner, was named as Lee Wright, who is not the father of the child.
Police have not confirmed the names of those under arrest.
They were downstairs when the attack took place, police said.
Locals claim to have made previous complaints about the dog's behaviour to police.
Chief Superintendent Chris Bithell of Lancashire Police said: "This is an absolutely horrific incident in which a baby girl has lost her life and I would like to take this opportunity to express my own personal sympathy to the wider family of baby Ava."
Mr Bithell said police were first alerted by the ambulance service who were called to reports of the girl being mauled by a pet dog.
A post mortem will take place to find out the exact cause of death.
Mr Bithell added: "The dog is believed to be an American Pit Bull type, it has been destroyed and tests will be carried out today to establish the exact breed of the dog and inquiries into the history of the animal.
"I'm told its quite a large pit bull type dog."
Both suspects were initially arrested on suspicion of child neglect, before being re-arrested this morning on the more serious charge of manslaughter and will be questioned by detectives today, Mr Bithell said.
"The lady in custody is the baby's mother and the male in custody is the mother's current boyfriend," he added.
"The baby was upstairs in a bed in one of the front bedrooms and the two people who are currently in custody, they were downstairs when the attack took place."
Asked about claims from neighbours reporting dangerous dogs at the address he added: "As part of the investigation we are making inquiries to see whether there have been previous issues with this particular dog and I think at this moment it would be too early to speculate on that."
Tributes were paid to the baby girl on Facebook.
Catt Allen wrote: "RIP Ava-Jayne heaven has gained another angel sleep tight beautiful girl xxxx".
Jodii-Rebekah Doran added: "RIP Ava-Jayne. Heaven has gained a beautiful angel xxx".
Derek Turner posted: "Absolute tragedy ! R I P Little angel xx".