A spokeswoman for Middlemore said the boy was now stable in the intensive care unit.
It is understood he suffered extensive facial injuries in Sunday's attack. The dog belonged to a member of his extended family, who are "deeply shocked".
The attack has been reported to the Western Bay of Plenty District Council and is being investigated by police.
Council spokesman Peter Hennessey said the dog, believed to be between 4- and 5-years-old, was an unregistered "border collie-type" and has been put down following the attack.
"The owner of the dog relinquished it to council," he said.
"The dog has been put down, eliminating the risk to public safety completely. This is not a breed usually associated with such attacks.
"In terms of a safety message, we can't reiterate enough the importance of ensuring children are never left unattended with a dog. Again, we also stress the importance of registering your dog."
The attack has prompted the New Zealand Association of Plastic Surgeons president Dr Sally Langley to call for tougher dog-control laws.
"This is life-changing. This will affect the child and his family's socialisation, his education and work potential. It is far reaching and there will be many psycho-social effects.
"We really do need to call for some action. The members of our society are all very concerned about the high incidences ... we have all done a lot of work with dog-bite victims, we regularly see them."
A study published in August reported that 99,000 dog bites have been recorded in the last 10 years. More than 5800 required hospitalisation.
Dr Langley said the Government needed to do more to ensure people were protected from dangerous dogs.
She was not directly involved in Sunday's case, but said the victim would likely suffer a lifetime of social and medical implications.
She believed the Government needed to look at whether certain dog breeds should be banned, and whether local governments were able to deal with issues sufficiently.
Under the Dog Control Act, all dogs are required to be registered and microchipped and kept under control and looked after. Some breeds are illegal to import.
Fees, penalties and dogs classified as dangerous are overseen by councils, but criminal action can also be taken through the courts.
National's Associate Local Government Minister, Louise Upston, said an assessment of the country's dog-control laws by the Department of Internal Affairs last year found no need for change.
"The conclusions were that New Zealand is not markedly out of step with other similar countries and further changes to dog-control regulations would not necessarily better protect people from harm," she said.
However, Labour's local government spokesman, Su'a William Sio, said current laws were failing to protect New Zealanders.
"If it's not working then it is high-time legislation. It doesn't give anyone confidence does it? The more these things keep happening the more we need to find proper solutions."
Dog attacks in NZ
• 99,000 dog bites in NZ since 2004.
• More than 5800 required hospitalisation.
• Nearly two-thirds occurred at private residences.
• Children under 9, Maori and those in low socio-economic areas are at greatest risk.
• Most children received facial injuries.
Source: The Burden of Dogbite Injuries in New Zealand: 2004-2014
Additional reporting: NZME
