The Sikh family were on en route to Hawke's Bay from Auckland Airport where family members who had travelled from Australia had been picked up when the accident took place yesterday morning.
The family's van was "pancaked" upside-down in the mishap that occurred on State Highway 5 about 80km from Napier, NZ Herald newspaper reported.
Jagtar Singh, who is in his 30s, was in the intensive care unit at Hawke's Bay Hospital.
His wife Sukhwinder Kaur, their two daughters aged 9 and 8, and baby Manmeet from Melbourne, in New Zealand to celebrate the birth of the first son in the family, also sustained injuries.
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Jagtar's brother Sandeep, who was driving the van, is understood to have been thrown from the vehicle with the baby and a passing motorist found them on the roadside following which he notified emergency services about the van at the bottom of the cliff.
A man in his 40s and a man in his 20s were described as being in stable condition.
All the eight persons in the van have been hospitalised.
"Traumatised" family members called Sikh priests into the intensive care unit to pray for the most critically injured victims of the crash.