The family's van was "pancaked" upside down in the mishap that occurred on State Highway 5, about 80 km from Napier, New Zealand 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 nine and eight, and infant boy Manmeet from Melbourne, in New Zealand to celebrate the birth of the first son in the family, also sustained injuries.
The baby's condition has, however, improved overnight and he is in a serious but stable condition in intensive care, TVNZ reported.
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 a stable condition.All eight persons in the van have been hospitalised. Traumatised family members called Sikh priests into the intensive care unit to pray for the critically injured victims of the crash.