The tremor, at a depth of 72 kilometers (45 miles), hit at 4:16 a.m. local time (17:16 GMT Thursday) 81 km south of the town of Panguna in Papua New Guinea.
The USGS issued a “green alert,” to say there was a low likelihood of casualties and damage.
In February the remote town of Lata was hit by a devastating tsunami after an 8.0-magnitude earthquake. The tsunami left at least 10 people dead, destroyed hundreds of homes and left thousands of people homeless.
The Solomons are part of the “Ring of Fire,” a zone of tectonic activity around the Pacific that is subject to frequent earthquakes and volcanic eruptions.
In 2007 a tsunami following an 8.0-magnitude earthquake killed at least 52 people in the Solomons and left thousands homeless.