The epicentre of the quake, which hit at 6:10 am, was located 90 kilometres west of Kirakira, a provincial capital in the Solomons, at a depth of 10 kilometres, the US Geological Survey said.
There is low likelihood of casualties and damage, it added.
The Pacific Tsunami Warning Centre said there was no tsunami threat from the quake.
It comes a day after a major 7.7-magnitude quake struck off the archipelago, triggering severe shaking and a tsunami warning, but there were no reports of any serious damage.
The Solomon Islands are part of the Pacific "Ring of Fire", a zone of tectonic activity known for frequent quakes and volcanic eruptions.