Peters and a delegation of other ministers were due to visit the capital Nouméa later this week.
Nouméa's La Tontouta International Airport is expected to remain closed until at least 5pm today (local time).
On Monday demonstrations, marches and confrontations with security forces spread throughout New Caledonia with hot points in suburbs of Nouméa.
By the evening, several violent confrontations were still taking place between pro-independence militants and police.
Officials were working to set a new date for the visit, Peters said.
New Caledonian airline Aircalin has also cancelled a flight due to leave Auckland for Nouméa on Tuesday afternoon.
Aircalin flight SB411 had been due to depart Auckland at 2pm.
The airline said rescheduling information would be posted on its website as soon as possible.
Aircalin flight SB410 from Nouméa was due to land in Auckland at 12.40pm on Tuesday, but it was not immediately clear if the aircraft had been able to leave before the airport shut down.
Auckland Airport's arrival board has no indication of the flight being cancelled.
Meanwhile, Air New Zealand is monitoring the situation ahead of its next flight to Noumea at 8.25am on Saturday, May 18.
A spokesperson for the airline said that flight was still expected to leave on schedule.
