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Emergency services were called to a house in the suburb of Enderley about 7pm on Sunday after the attack.
The baby died overnight on Monday.
"Sadly, yes - the baby passed away," police confirmed on Tuesday.
"The matter will be referred to the coroner."
The baby was initially taken to Waikato Hospital by ambulance in a critical condition.
Hamilton City Council staff collected the dog soon after the attack and it is at the city pound.
It is not yet known if the animal will be put down.
Police say inquiries into the circumstances of the incident are continuing.