The Defence Force Hercules has about 57 people on board.
Another 110 New Zealanders are still in New Caledonia waiting to get home.
Foreign Affairs Minister Winston Peters confirmed the flight on X (formerly Twitter), saying the plane was scheduled to land in Auckland later on Saturday.
It will be the fourth repatriation flight since fatal clashes broke out between pro-independence protesters and security forces.
Protesters fear that electoral reform will dilute the votes of indigenous Kanaks, who make up 40% of the island's population of 270,000 people.
In the latest developments, a police officer reportedly shot and killed a man after he and a colleague were attacked by a group of about 15 people.
It comes just a day after French President Emmanuel Macron visited the territory in a bid to calm tensions.
Meanwhile, a New Zealander evacuated from New Caledonia said parts of the capital were like a bomb site.
Andre Capiez was one of about 50 people who were on the third evacuation flight from Nouméa.
Capiez, born in New Caledonia, said most of the damage in the capital could not be seen from tourist areas.
"In parts of the city it's like, amazing. I mean, you know [if you've seen] pictures of bombed areas, that's what it looks like. Everything's been burned down and looted..."
People on both sides of the civil unrest did not condone the violence, Capiez said.
The death toll from the civil unrest is now seven.
