The US Geological Survey initially measured the quake at 6.7-magnitude but later revised it down to 6.3 at a depth of 19 kilometres.
"We've got it at 6.6," Geoscience Australia seismologist Jonathan Bathgate said, adding that the quake was "very unlikely" to have generated a tsunami.
A separate bulletin from the the Hawaii-based Pacific Tsunami Warning Center also ruled out the threat of a Pacific-wide destructive tsunami.
The Solomon Islands are part of the "Ring of Fire", a zone of tectonic activity around the Pacific Ocean that is subject to earthquakes and volcanic eruptions.
In 2007 a tsunami following an 8.1-magnitude earthquake killed at least 52 people in the Solomons and left thousands homeless.
Bathgate said the latest tremors follow two 6.1-magnitude quakes and one 6.4-magnitude in the same area over the past few days.
"There's been four quakes over six (magnitude) in the last three days in that area. It doesn't necessarily indicate that there's anything bigger to come. There could be some more to come or there could be nothing. We just don't know."