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.
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.
The wave in Lata came 18 minutes after the quake.
The tsunami has also hit New Caledonia's eastern coast with a 55 centimetre wave.
On Vanuatu's Santo island, the wave measured 26 centimetres.
The Fiji authorities advised all residents on low-lying coastal areas to evacuate to higher zones as soon as possible.
The Solomon Islands police commissioner, John Lansley, says they have received some damage reports from Temotu Province.
"Well we know there has been an impact, a slight impact in Temotu near Lata near Santa Cruz. We believe that one of the islands called Lord Howe has been affected. We don't know the extent of how they have been affected. We believe there is some house damage at least - we are not sure about loss of life. We are trying to evaluate that. We are currently preparing for a possible surge as they call it, so we are at the moment we are sending general information out to the population of Honiara and other provinces, including Auki, Kirakira and other areas in the Solomon Islands."
The Vanuatu Disaster Management Office says people in coastal northern have been told to move to higher ground.
A spokesman for the office Sylvain Todman says there are reports from the northern island of Santo that the initial quake was felt strongly and there was a series of aftershocks.
The Fiji authorities have advised all residents on low-lying coastal areas to evacuate to higher zones as soon as possible.