Heavy rainfall and flash flooding was forecast for Torba, Sanma, Malampa and Penama provinces, especially in low lying areas and areas close to river banks.
Landslides and coastal flooding were also a possibility, according to the service.
Donna was sitting just north of the Island on Saturday night.
The worst of cyclone was expected to bypass New Zealand, MetService said, however Noumea in New Caledonia, was at risk of a direct hit early next week.
A cyclone "pre-warning" has been issued by the government in New Caledonia.
"Donna should intensify again on Sunday and bend its trajectory towards the South-East," the government stated on its website.
"It will be about 600km north-west of Port-Vila and 625km in the north of Belep, late night from Saturday to Sunday."
Owners of coastal properties in Vanuatu told WeatherWatch.co.nz on Thursday that they'd already started battening down the hatches in preparation for the storm.
Red Cross and World Vision volunteers are on the ground in Vanuatu and ready to help those affected when they need assistance.
World Vision Vanuatu country director Mike Wolfe told NZME since Cyclone Pam, staff had been working with communities on "how they're going to be prepared for disaster, and what they're going to do in times of disaster".
"We're really concerned about children and families being more vulnerable due to impacts to drinking water and shelter," he said.
The exact path of the storm is unclear, WeatherWatch.co.nz said, because "the South Pacific islands is possibly the trickiest place on earth" to track a storm's path.
"Cyclones in this area tend to meander a lot and cross back on themselves in the same unpredictable way a coin, once spun on a table top, can move around with a mind of its own.
"Tracking a cyclone around small islands is very hard - almost like hitting a hole in one when playing golf. When it's a larger nation like Australia or the USA then the storm has an enormously greater chance of hitting land."
