The baby boy was attacked by the dog, a small terrier, at an address in Falkland Road, Sunderland, police said. He was taken to hospital but later died.
A 30-year-old man has been arrested in connection with the incident and is helping police with their inquiries.
The dog has been removed from the address, and is likely to be destroyed, a police spokesperson said.
Police were called to the address at 4:15 am on Saturday.
Superintendent Gillian Mitchell said: “This is obviously a very tragic incident and our thoughts are with the family of the baby at such a difficult time.
“We are carrying out enquiries to establish the circumstances of the incident and will have extra officers in the area to allow this to be done.
“Officers will also be on patrol to offer reassurance to the local community who may be concerned.”