Tropical Cyclone Freda is currently south of the Rennell Islands in the Solomon Islands.
The category four system is weakening as it heads south, south east at about 13 kilometres per hour.
On Saturday Freda moved across the southern Solomons, bringing heavy rains and winds up to 130 kilometres an hour.
Witnesses say the cyclone tore roofs off houses and flattened trees.
The director of the National Disaster Management Office, Loti Yates, says thousands of people from riverside villages moved to higher ground.
There were no reports of injury.
Shalwin Singh from the Fiji Tropical Cyclone Centre says Freda will still make its presence felt in New Caledonia despite continuing to weaken on approach.
"It is expected to drift southwards in the coming few days. By the time it approaches New Caledonia it is expected to weaken to a category two cyclone, so most probably they will start experiencing gale force winds by the 2nd of January."
Earlier this month Cyclone Evan strengthened to a category four cyclone and left a swathe of devastation in its wake, destroying homes, flooding rivers and stranding thousands of tourists in Fiji.
A United Nations situation report says more than 1,200 people remain in evacuations across Fiji, down from more than 11,600 on December 20.
Before arriving in Fiji, the cyclone pummelled neighbouring Samoa, killing at least five people.
Cyclone Evan affected 12,600 people with housing damages, according to the UN’s Office for the Coordination of Humanitarian Affairs.