The United States Geological Survey said the tremor, at a depth of 13 kilometres (eight miles), struck in the Santa Cruz Islands at 0643 GMT about 93 kilometres southwest of Lata.
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.
"There's nothing to worry about," Geoscience Australia duty seismologist David Jepsen told AFP after the latest earthquake, adding that his agency estimated it at magnitude 6.0.
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.
