Fiji is on a tsunami watch as the first large waves generated by the 8.0 magnitude quake that struck near the Solomon Islands at around 1pm, are expected to hit low-lying areas at around 4pm today.
The government has asked those living in low-lying areas to move to higher ground.
The Pacific Tsunami Warning Centre said a tsunami could be destructive near the epicentre of the earthquake.
"Sea level readings indicate a tsunami was generated,'' the Hawaii-based centre said.
"It may have been destructive along coasts near the earthquake epicentre and could also be a threat to more distant coasts."
Residents in the Solomons capital Honiara, 580 kilometres from the epicentre, told AFP the quake was not felt there, but some villages were destroyed, according to a hospital director.
"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 at Lata Hospital on the main Santa Cruz island of Ndende, told AFP.
A staff member at the Solomons 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 said first reports from the area were that there was a tsunami wave.
The tsunami warning from the Pacific Tsunami Warning Center in Hawaii is in effect for the Solomon islands, Vanuatu, Nauru, PNG, Tuvalu, New Caledonia, Kosrae, Fiji, Kiribati, Wallis and Futuna, Marshall islands, Howland and Baker, Pohnpei and Tokelau.
The powerful earthquake struck east of the Solomon Islands at 1.07pm today, at a depth of 5.8km. The epicentre was 347km east of Kira Kira in the Solomon Islands.