Tropical Cyclone Freda is located off northern New Caledonia, moving south-southeast at about 10 kilometres an hour.
The category two storm is generating sustained winds at the centre of around 110 kilometres an hour.
The Tropical Cyclone Warning Centre at the Fiji Met Service says the cyclone is expected to weaken further as it moves parallel along New Caledonia's west coast over the next few days.
Cyclone Freda hit the most southern parts of Solomon Islands over the weekend.
The duty forecaster at the weather office in Fiji, Shalwin Singh, told Radio Australia's that Freda could still bring very bad weather to New Caledonia.
"They will experience experience damaging gale force winds or stronger possibly for the next three days because the cyclone is moving really slow," he said.
"On the 3rd of January we expect it to lie to the west of New Caledonia. So it will affect New Caledonia for the coming few days."
On Monday Rajneel Prasad from the Tropical Cyclone Warning Centre in Nadi said Cyclone Freda could generate a storm surge as it moves south and affect low-lying areas, especially the small islands in New Caledonia.
Mr Prasad told Pacific Beat although the Freda is expected to weaken as it approaches the French Pacific territory, the storm's "intensity and strength" should not be underestimated.
Freda moved across the southern Solomons on Saturday, 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.
© ABC 2013
16:38 EST Organisers of the Mulga Bill Quick Shear at Yeoval, in Central West New South Wales on the weekend, were a bit nervous about the weather on Saturday morning; there'd been good rain on Friday night and they didn't have a 'Plan B' if things didn't clear up.