The cyclone caused flooding in Vanuatu's central islands yesterday and is now set to hit New Caledonia's main island.
The storm's centre is forecast to pass to the west of the Loyalty Islands, before making landfall on the east coast of the main island Grand Terre.
Cyclone Cook will be the first to directly hit New Caledonia since 2003.
A level-one alert is in force for New Caledonia's north and outer island, meaning properties and livestock should be secured.
At lunch time, a level-two alert will come into force, which means people have to be inside their homes or shelters and all movement is banned.
For New Caledonia's south, which includes the capital Noumea, a level-one alert comes into force at midday and a level-two alert at 8pm tonight.
Meteo France said the threat was very serious, forecasting gusts of up 200 kilometres an hour.
Rain fall of 350 millimetres is predicted for a 24-hour period.
All domestic flights have been cancelled for today and tomorrow.
The adverse weather conditions in New Caledonia have prompted the French education ministry to cancel some exams nationwide because it is unsafe for those in the territory to go their tests.
Photo: RSMC Nadi Tropical Cyclone Warning Centre Cyclone Cook forecast to intensify to category 4