The quake’s epicentre was in the ocean about 56 kilometres southwest of the capital, Honiara, at a depth of 13 kilometres, according to the United States Geological Survey.
There were no immediate reports of widespread damage or injuries.
The US Tsunami Warning System said the earthquake hit around 1pm and is now warning there is a tsunami risk.
“Hazardous tsunami waves possible for coasts within 300 kilometres of earthquake epicentre,” it said.
The US Tsunami Warning System added Honiara, Kirakira, Auki and Ghatere are at risk over the coming hours.
The earthquake may produce waves of up to one metre above tide levels for the Solomon Islands, the Pacific Tsunami Warning Centre said, and smaller waves for the coasts of Papua New Guinea and Vanuatu.
The body also warned coastal areas at risk in this radius should stay alert and follow instructions from national and local authorities.
The Solomon Islands sit on the Pacific Ring of Fire, an arc along the Pacific Ocean rim where many volcanic eruptions and earthquakes occur.
The Bureau of Meteorology said there is no tsunami threat to Australia.