The tsunami waves were observed at Maré Island in New Caledonia and Lenakel in Vanuatu. There is a tsunami alert for New Caledonia, Vanuatu and Fiji. People in coastal areas were reportedly urged to evacuate immediately and these evacuations are underway.
New Caledonia is French territory in the South Pacific.
The undersea quake was only a shallow 10km (6miles) deep and about 155km (95miles) east-southeast off New Caledonia’s east coast.
There is no news yet on damage.
Hazardous tsunami waves are forecast for some coastlines.
“Hazardous tsunami waves from this earthquake are possible within 1,000 km (600 miles) of the epicenter along the coasts of Vanuatu and New Caledonia,” the PTWC said.
Just four minutes earlier a 6.0 magnitude earthquake struck just 147km away from the island.
Around 284,000 people are expected to be affected, including in the cities of Tadine, Vao and We.
Tsunami waves 1 to 3 metres high are possible along the coast of New Caledonia and up to 1 metre in Fiji.
There were two more aftershocks – one measuring 5.9 on the richter scale 142km from New Caledonia, one at 5.7 magnitude and 131km away from New Caledonia.
New Caledonia is made up of a group of islands to the east of Australia.
It has been part of France since 1853 and last month its residents voted to remain French in a referendum.
A spokesman for French mining and metals group Eramet, which has a nickel plant in te harbour of Noumea, New Caledonia, said it enacted its tsunami alert process.
He said: “The procedure is to ask people who work near the sea to move higher up,” he said.
The spokesan added that he had felt the quake, describing it a strong but not long-lasting shaking.