The Pacific Tsunami Warning Centre initially said there could be possible "widespread, hazardous" tsunami waves, forcing villagers to flee to higher ground.
But within three hours the warning was downgraded after the threat passed without major incident.
The epicentre of the quake, which hit at 4:38 AM, was located 68 kilometres (42 miles) west of Kirakira, a provincial capital in the Solomon Islands, at a depth of 48 kilometres, the US Geological Survey (USGS) said.
Donald Tehimae, an officer at the Kirakira police station, said most of the damage appeared to be superficial.
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"Some houses have been damaged but no one was hurt. At the police station a lot of documents in the storeroom fell down," he said.
Suzy Sainovski, an official with aid organisation World Vision in the capital Honiara, said the shaking was frightening.
"The earthquake woke me up. I was in bed and it was dark and it felt like being in a matchbox that someone was just shaking and shaking," she told AFP.
"Just from briefly looking outside my window as it begins to get light, I didn't see any damage to buildings."
Hugh Glanville, duty seismologist at Geoscience Australia, said the offshore epicentre of the earthquake and sparsely populated areas helped minimise the impact.
"So far we have had no reports of major damage," he told AFP.
"There was a small tsunami, the waves were under half a metre. They've arrived through most of the Solomons and Vanuatu and the threat level is diminished or has passed.
USGS said earlier that some casualties and damage were possible from the quake, warning that waves reaching 1-3 metres above tide level could occur along parts of the Solomons.
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