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 (1738 GMT Thursday), 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.
Electricity supplies were cut in some areas and there were reports of thatched houses collapsing.
Donald Tehimae, an officer at the Kirakira police station, said most of the damage appeared to be superficial.
"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.
"It felt almost like the hotel's foundation was just moving in waves. The shaking felt like it went on for quite a while -- 30 to 45 seconds. The cupboard doors were shaking, but nothing fell over.
"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.
"The reason we often get so little damage from big earthquakes in this area is that the plate boundary is offshore," he added. "The epicentre being 100 kilometres offshore makes all the difference."
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.
It had also warned some coasts in Vanuatu, Papua New Guinea, Nauru, New Caledonia, Tuvalu and Kosrae, as well as Hawaii, were at risk, before saying the threat had passed.
The earthquake-prone Solomon Islands, east of Papua New Guinea and with a population of more than 500,000, are well rehearsed in what action to take following several devastating tremors.
In 2007, an 8.0 magnitude quake claimed 52 lives and left thousands homeless when it created a 10-metre (33-feet) tsunami.
At least 10 people died when another 8.0 quake in 2013 caused widespread property damage.
The Solomon Islands are part of the Pacific "Ring of Fire", a zone of tectonic activity known for frequent quakes and volcanic eruptions.
It is one of the most seismically active parts of the world.