The quake struck at a depth of 5.8km at 11.07am AEDT on Wednesday, near the Santa Cruz Islands, which are part of the Solomon Islands nation. 

The director at Lata Hospital on the main Santa Cruz island of Ndende said villages had been destroyed by the quake.

"The information we are getting is that some villages west and south of Lata along the coast have been destroyed, although we cannot confirm this yet,’’ the director said.

A tsunami measuring 91 centimetres in height was recorded at Lata Wharf in Santa Cruz Islands, near the epicenter, and an 11-centimeter wave was recorded in Luganville, Vanuatu.

The tsunami would have hit nearby islands "within a matter of minutes", said Rick Bailey, head of tsunami warning services at Australia’s Bureau of Meteorology.

The Solomons capital Honiara, about 600km from the epicentre, recorded a wave of seven centimetres about an hour later, Mr Bailey said.

Earlier, the Pacific Tsunami Warning Centre issued a tsunami warning for the Solomon Islands, Vanuatu, Nauru, Papua New Guinea, Tuvalu, New Caledonia, Kosrae, Fiji, Kiribati, Wallis and Futuna.

Mr Bailey said the quake was not large enough to generate waves to reach Australia's coast.

The Solomon Islands' National Disaster Management office said officials were concerned about the eastern province of Temotu.

"That’s the province, which if it is going to have an effect, then they will be the first people to be impacted," the official, who did not wish to be named, told AFP. "They felt the quake."

He added that the national disaster operation centre had been activated and they were trying to contact those in Temotu province.

Australia’s Department of Foreign Affairs and Trade said it was “monitoring any possible impact on both life and infrastructure”.“Early reports suggest there is some damage to low-lying areas in Lata, including the airport,” the department said in a statement. “So far there are no reports of damage to Honiara.”

''Our Embassies and High Commissions in the region are aware of the possible tsunami and are liaising with local authorities, hotels and other locations were Australians may be located. We recommend that Australians in the region continue to monitor local media and follow the advice of local authorities.”

Solomons deputy opposition leader Matthew Wale told Fairfax Media citizens in Honiara had moved to higher ground in anticipation of the tsunami.

‘‘There is no panic, people aren’t running. They are making their way in an orderly fashion.

‘‘Most of the shops and offices have shut and people are milling about on their way to higher ground,’’ he said.

The quake was placed 70 kilometres west of Lata and nearly 600 kilometres from the national capital, Honiara.

But an Australian working in Honiara first learned of the earthquake when contacted by Fairfax Media.

"There is no panic on the streets. People are going on like any normal day," he said.

"We really have not heard anything about it nor that there is an imminent threat. Everything seems calm as usual."

Geoscience Australia estimated the quake could have been felt 836km from the epicentre and caused damage up to 67km away.

The Solomon Islands form part of the Ring of Fire, a zone of tectonic activity around the Pacific Ocean that is subject to earthquakes and volcanic eruptions.

Australians seeking consular assistance should call +61 2 6261 3305 from outside Australia or 1300 555 135 from within Australia.

Megan Levy, with Ilya Gridneff, Peter Hannam, AFP and Reuters