Police say there are "concerns" over his scalp and face injuries.
The dogs have been taken away by Christchurch City Council animal control officers and will be put down.
A spokeswoman for the council said the family today "voluntarily surrendered" the dogs to the council for euthanasia.
The boy had "significant" injuries, said police Inspector Derek Erasmus.
"It was a vicious attack. His sister says the dogs had been throwing the boy in the air," he said.
The family are assisting police with their ongoing investigation, he said, which will determine whether the owners will be charged.
"We are interviewing witnesses and monitoring the condition of the child," said Mr Erasmus.
"But they are more concerned about their child. He's still in hospital and likely to be for a few more days.
"There is concern about the injuries to his head and face as well as the injuries to his leg."
A spokeswoman for Canterbury District Health Board said they could not provide a condition update because the boy's family had asked for "complete privacy''.
One local resident, who did not wish to be named, said there were a lot of dog owners in the area.
He wasn't aware of Saturday's attack, but said it explained the high level of activity by dog control in the neighbourhood over the weekend.
Another elderly resident said: "Too many dogs roam free around here. They have the run of the place."
The attack comes after Chloe Jane Mathewson, 31, was mauled to death by two large rottweilers in Redvale near Auckland in March.
It's believed there have been six recorded fatal dog attacks in New Zealand.
