The US Geological Survey said quake struck at 10:04 am local time (2304 GMT Thursday) at a depth of 33 kilometres (20 miles) some 70 kilometres west of Kirakira -- the same region where several large tremors struck last month.
The Hawaii-based Pacific Tsunami Warning Center said there was no tsunami threat from the latest shake.
Three strong tremors were felt off Kirakira in December without causing serious damage.
The Solomons National Disaster Management Office (NDMO) said it had not received any damage reports from the remote area.
"We haven't had any information come through," NDMO director Loti Yates told AFP from the capital Honiara.
The Solomon Islands are part of the Pacific "Ring of Fire", a zone of tectonic activity known for frequent quakes and volcanic eruptions.
In 2007 an 8.0-magnitude quake in the Solomon Islands claimed 52 lives and left thousands homeless when it created a 10-metre tsunami.
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