The US Geological Survey said the tremor, at a depth of 70 kilometres (43 miles), struck in the Solomon Sea at 3:32 am local time (17:32 GMT today) about 84 kilometres southwest of Chirovanga.
The USGS PAGER (Prompt Assessment of Global Earthquakes for Response) issued a green alert level projecting a very low risk of casualties or economic losses.
In February the remote town of Lata was hit by a devastating tsunami after a 8.0-magnitude earthquake. The tsunami left at least 10 people dead, destroyed hundreds of homes and left thousands of people homeless.
In 2007 a tsunami following an 8.0-magnitude earthquake killed at least 52 people in the Solomons and left thousands homeless.