The US Geological Survey said the moderate quake struck at about 4:26am (local time).
Its epicentre was located in the ocean 70 kilometres south-southeast of Chirovanga, 424 kilometres from the capital Honiara.
There were no immediate reports of damage after the quake.
In 2013, the islands were struck by a major 8.0 magnitude quake that generated small but deadly tsunami waves which washed away houses and reached as far away as Japan.
The Solomons are part of the "Ring of Fire", a zone of tectonic activity around the Pacific that is subject to earthquakes and volcanic eruptions.
In December 2004, a 9.3-magnitude quake off Indonesia triggered a catastrophic tsunami that killed 226,000 people around the Indian Ocean.