The US Geological Survey said the quake was measured at a depth of about 10 kilometres and struck 160 kilometres southeast of the town of Gizo at 1419 GMT Sunday.
Like much of the Pacific, the Solomons regularly experience earthquakes.
A string of earthquakes rocked the western Solomon Islands earlier in the month, with the largest of 7.2 causing a tsunami estimated at eight feet.
Around 1,000 people -- almost a third of the population -- are believed to have been left homeless on Rendova island due to earthquake and tsunami damage.
In April 2007, an 8.0-magnitude earthquake in the western Solomons triggered a tsunami that killed more than 50 people and displaced thousands. Gizo harbour lost most of its wharves and jetties in the quake and subsequent tsunami.
