The shallow quake was centred some 186 kilometres southwest of Dadali and 214 kilometres from the capital Honiara.
The Hawaii-based Pacific Tsunami Warning Center, which also measured the quake at 6.9, said "a destructive Pacific-wide tsunami is not expected".
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"They would definitely have felt it over quite a wide area, over hundreds of kilometres," Geoscience's duty seismologist Hugh Glanville said of residents of the Solomon Islands.
"But there shouldn't be a tsunami and hopefully not too much damage," he told AFP.
Glanville said the fact that the epicentre was some distance from the Solomons' main population centres and was undersea rather than on land would also limit any impact.
The Solomons are part of the Pacific "Ring of Fire", a zone of tectonic activity known for its frequent earthquakes and volcanic eruptions and Glanville said these kinds of tremors were "common in the region".
It is one of the most active seismic regions in the world with a 7.0-magnitude quake striking 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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