The quake struck near the Santa Cruz islands at a depth of 33 kilometres just before 1.30pm local time.
A spokesperson for the police in the provincial capital Lata, 75 kilometres west of the epicentre, says the violent shaking lasted about two minutes.
He says crowds gathered at a football tournament in town ran to seek shelter on a nearby plateau after a tsunami warning was issued.
That warning was later cancelled, but the policeman says the sea rose by about 20 centimetres and changed colour from blue to green.
The spokesperson says there is no significant damage in Lata, but police are yet to hear from more remote and less-developed parts of the province.
The province was hit by a magnitude eight earthquake in February 2013, which triggered a tsunami that smashed through seaside villages, killing at least 10 people and destroying houses, crops and infrastructure.
The Pacific Tsunami Warning Center in Hawaii issued a warning, saying “hazardous tsunami waves from this earthquake are possible within 300km of the epicentre along the coasts of the Solomon Islands”.
But 30 minutes later, the Centre said there was no longer a tsunami threat, but that small sea level fluctuations above and below the normal tide may continue for a few hours.