The quake struck at 8:05 am (local time) at a depth of 54 kilometres around 260 kilometres east of the capital Honiara, according to the United States Geological Survey.
GeoScience Australia said damage would have occurred within a 37 kilometre radius and there were no immediate reports of any destruction.
In 2007 a tsunami following an 8.1-magnitude earthquake killed at least 52 people in the Solomon Islands and left thousands homeless.