The quake hit at 7:19 pm local time (0819 GMT), 176 kilometres (110 miles) southeast of the capital Honiara at a depth of 54 kilometres, the US Geological Survey said.
The Hawaii-based Pacific Tsunami Warning Center said there was "no destructive widespread tsunami threat" based on historical data.
"However, earthquakes of this size sometimes generate local tsunamis that can be destructive along coasts located within a hundred kilometres of the earthquake epicentre," it added.
The Solomon Islands is on a tectonic plate margin in the so-called Pacific Ring of Fire and is frequently hit by quakes. A strong 6.6-magnitude quake hit the island group in January but there were no reports of damage or injuries.
In 2007 a tsunami hit the Western Solomons following an 8.1-magnitude earthquake which killed at least 52 people and left many homeless.
6.5 Earthquake Hits Solomons
A strong 6.5-magnitude earthquake shook the Solomon Islands late yesterday afternoon, but there was no threat of a widespread destructive tsunami and no reports of damage, US seismologists said.
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