A small tsunami wave reached part of the Solomons and watches were in effect as far afield as Hawaii, the Pacific Tsunami Warning Centre said.
New Zealand was also on guard, but monitors said there was no threat to Australia. The US Geological Survey said the quake struck at 0112 GMT near the Santa Cruz Islands in the Solomons, which have been hit by a series of strong tremors over the past week, at a depth of 5.8 kilometres.
Two powerful aftershocks of 6.4 and 6.6 magnitude were also recorded. "Sea level readings indicate a tsunami was generated," the Hawaii-based Pacific centre said.
"It may have been destructive along coasts near the earthquake epicentre and could also be a threat to more distant coasts."
Australia's earthquake monitoring agency and the Pacific centre said a wave measuring three feet had been recorded at Lata, on the main Santa Cruz island of Ndende.
"We know that a tsunami has been created," Geoscience Australia seismologist David Jepsen told AFP.
He said depending on the location of the quake, bigger waves could hit elsewhere. "It's a big earthquake anyway in terms of just the shaking," he said.
Locals in the Solomons capital Honiara, 580 kilometres from the epicentre, said the quake was not felt there, but some villages on the Santa Cruz islands 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 of nursing at Lata Hospital told AFP.
"There was continuous shaking in Lata but no damaged buildings here," he added.