By Agence France-Presse
The quake struck 164 kilometres (101 miles) from the capital Honiara at a depth of 35 kilometres -- the fourth big tremor is just over a week.
"Based on all available data, a destructive Pacific-wide tsunami is not expected," the Pacific Tsunami Warning Center said, while Geoscience Australia estimated damage would only be likely up to 74 kilometres away.
The Solomon Islands are part of the Pacific "Ring of Fire", a zone of tectonic activity known for frequent quakes and volcanic eruptions.
On December 9, a 7.7-magnitude tremor triggered severe shaking and a tsunami warning in the same area, although there were no reports of serious damage. This was followed by a 6.9-magnitude aftershock a day later and another of 6.0 magnitude on Sunday.