The Pacific tsunami warning centre says a 90 centimetre wave has been measured in Lata in Solomon Islands Temotu province after a strong earthquake.
The US geological survey says the quake measured 8 on the Richter scale.
Its centre was 29 kilometres deep.
The accountant at Lata Hospital, Moses Mekupe, says several people have been admitted with injuries after the earthquake and tsunami.
Speaking three hours after the quake he said tremors were continuing and most people had moved inland.
He told our reporter about the initial quake.
"All of us were in our offices. Suddenly the earthquake strikes and it runs about five minutes and then a tsunami later hits areas around Lata."
Mr Mekupe says the tsunami came immediately after the quake.
He says while Lata was not damaged there has been destruction in coastal communities near the main town.
The impact was some communities or houses swept away, near communities, but far communities we are still to hear information.
Mr Mekupe says there have been three admissions to hospital.
At the moment three injuries. One with a broken arm and the other two with broken legs.
A tsunami warning has now been cancelled.
It had been in force for Solomon Islands, Vanuatu, Nauru, Papua New Guinea, New Caledonia, the Federated States of Micronesia, Fiji and Wallis and Futuna.
Authorities in New Caledonia say the territory remains on alert for damaging waves until 0530 UTC following the Solomon Islands earthquake.
A 55 centimetre wave was measured at at Hienghene in the Northern Province, and a 48 centimetre wave hit Lifou in the Loyalty Islands.
A spokesperson at the French High Commission in Noumea Leatitia Giachetti says people were asked to move away from all of the territory's coastal areas following the alert.
She says no damage has been reported.
On Vanuatu's Santo island, the wave measured 26 centimetres.