The family's American Staffordshire terrier had attacked their neighbour's dog just weeks before the tragic death.
The five-week-old tot died at his family's home on Jeffs Close in Kariong on the NSW Central Coast, Australia, about 2.18am on Sunday
Emergency services rushed to the scene and tried to revive the little boy but he was declared dead at the scene.
A crime scene was established, though police concluded there were no suspicious circumstances.
Detective Superintendent Darryl Jobson has described the awful situation as a "matter of tragic proportions".
He confirmed that the fatal mauling of the baby was not the first attack by the family dog in the last month.
Speaking on Sunday afternoon he said: "A neighbouring dog apparently got into the rear yard and was mauled by this dog, unfortunately.
"That was a separate incident but that will also form part of our investigation."
Superintendent Jabson also explained that all first responders who attended the scene would be receiving counselling and support after witnessing the horror incident.
He added: "Our police did perform first-aid upon arrival. They did their best in the circumstances and they are no doubt shaken by the incident.
"Anything to do with children of any type, particularly of this nature, is absolutely traumatic."
The parents of the tot were at home when their son was mauled by the dog, which has since been impounded.
His death is not being treated as suspicious and a report will be prepared for the coroner.
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