A 24-year-old man and a 20-year-old woman have been arrested on suspicion of child neglect and are in police custody.
The unnamed baby was taken to Royal Blackburn Hospital from a home in Blackburn, Lancashire, yesterday and later died, the 'Daily Express' reported.
The dog was seized from the address by Lancashire Police, who are yet to confirm its breed.
Detective Superintendent Simon Giles said: "This is a tragic incident and specially trained officers are offering support to the wider family."
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The relationship between the baby and those arrested has not been confirmed, the paper said.
The death of the baby girl comes after a spate of similar attacks in recent years.
In December last year, a 27-year-old woman in Leeds was savaged at home by two dogs.
In November 2013, a four-year-old girl was mauled to death by her pet dog in Leicestershire.
Last year, the UK government proposed that owners of dogs that attack and kill people will face 14 years in jail under tough new laws.
According to the proposed rules, if a dog injures someone in an attack its owner could be imprisoned for five years, and if a guide dog is attacked the penalty would be three years in jail.