It is understood runway debris is especially dangerous for jet aircraft that could suck it into their engines. Air New Zealand flies Airbus A320s to Vanuatu.
Other carriers including Air Vanuatu Virgin Australia, Fiji Airways and Air Caledonie International also fly there.
Air New Zealand customer care spokeswoman Debbie McKeown said this would inconvenience customers but safety came first.
"Unfortunately we will only be able to carry customers who are completing a return journey on Sunday's flights. We have put a comprehensive customer plan in place."
The airline would contact passengers who have booked directly with Air New Zealand to explain their options.
"Customers who've booked through a travel agent should make contact with their travel arranger. All customers will have the option of changing their booking to another Pacific or Tasman destination or receiving a full refund."
Air New Zealand has been operating to Vanuatu once a week and codesharing with Air Vanuatu on its twice weekly Auckland-Vanuatu services.
Today's decision affects Air New Zealand operated services and codeshare bookings made via Air New Zealand on Air Vanuatu operated services.
Vanuatu was ravaged by Cyclone Pam last January but had been showing signs of recovery, according to a RNZ report.
A snap election being held today was triggered last month when the president, Baldwin Lonsdale, dissolved parliament to end weeks of political instability following the conviction of 15 MPs for corruption.
Simon McKearney from travel agency HelloWorld said the decision would be disruptive but it was a case of safety first.
From their point of view they're going to
"It's ashame because they have recovered quite well l from the cyclone but to be hit by something like this," he said.
"You can't argue against it because Air New Zealand is impeccable with their safety . From a Vanuatu point of view it is a bit tragic. It makes it tough for the small economy they've got, said McKearney.
Flight Centre's NZ general product manager Sean Berenson said he hoped the necessary repairs for the runaway at Port Vila International Airport were made soon so that Air New Zealand is able to resume services.
"There are still alternative carriers operating flights and so we recommend anyone considering travelling to Vanuatu speak to their travel expert to explore options as soon as possible."
Visiting Vanuatu by ship is also a popular means of exploring the islands and with many ships departing Auckland and Australia a cruise is also a good alternative for anyone that would like to visit.