The quake struck at 8:05 am (2205 GMT Wednesday) at a depth of 54 kilometres (33 miles) around 260 kilometres (160 miles) east of the capital Honiara, according to the US Geological Survey.
GeoScience Australia said damage would have occurred within a 37 kilometre (22 mile) radius and there were were no immediate reports of any destruction.
"It was too small to create a tsunami," a GeoScience official said.
"Some small townships may have felt a moderate shake, but for most of the population it will have been just another quake. They have stacks of them out there.
"We`re 99.9 percent sure there will be no damage."
In 2007 a tsunami following an 8.1-magnitude earthquake killed at least 52 people in the Solomon Islands and left thousands homeless.
(U.S008/H-AK)
Editor: Priyambodo RH
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