The shallow quake reported past 1 a.m. local time struck at a depth of 3.6 miles off the region's Santa Cruz Islands.
The Pacific Tsunami Warning Center in Hawaii issued a tsunami warning for the Solomon Islands, Vanuatu, Nauru, Papua New Guinea, Tuvalu, New Caledonia, Kosrae, Fiji, Kiribati, Wallis and Futuna.
The center posted a tsunami watch for other areas in the region, including New Zealand, Australia, Indonesia, Marshall Islands, American Samoa and Guam.
There was no immediate report of injuries. TVNZ reported some patients at the Lata Hospital in the Solomons had been moved to higher ground.