The quake struck some 214 kilometres (132 miles) west of the town of Lata but 460 kilometres from the capital Honiara, USGS said.
"Based on all the available data a destructive Pacific-wide tsunami is not expected," the Pacific Tsunami Warning Centre said in an advisory.
The Solomons are part of the Pacific "Ring of Fire", a zone of tectonic activity known for frequent quakes and volcanic eruptions.
A 6.9-magnitude undersea tremor rocked the capital Honiara on Monday with no reports of serious damage.
It followed a a 7.0-magnitude quake which struck last month off the coast of the island chain. No damage from that tremor was reported.
However, in 2013, 10 people died and thousands were left homeless when buildings were destroyed after the Solomons were hit by a tsunami following an 8.0-magnitude quake.
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