The United States Geological Survey says the large tremor hit 63 kilometres south-west of Kirakira at a depth of about 49 kilometres.
Initially reported to be of magnitude 8.0, the area is experiencing a number of aftershocks exceeding magnitude 5.
The Survey's John Bellini says it may have further effects in the region.
"Because it was a large size, it has the potential for some significant damage. We don't have any specific reports of that at this time, but it is located relatively close to one of the islands there, I'm not sure the infrastructure situation, but it does have the potential to cause some damage."
The US-based Pacific Tsunami Warning Center has cancelled an earlier tsunami warning for the region.
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Dorothy Wickham is a freelance journalist based in the Solomons capital, Honiara.
Ms Wickham says she's heard reports of minor damage caused by the quake.
"I just spoke to police officers based in KiraKira and they said that from what they've seen so far, there's been some huts damaged, but no permanent buildings damaged and they will still be checking around for any more reports."
Dorothy Wickham says residents of the Solomon Islands are better prepared for earthquakes because of the frequency of their occurrence in the region.
"As you know we've had two tsunamis over the last decade. The understanding of earthquakes is much better than it was say 15 years ago, and this morning my family and I went up to the hills behind us, basically the whole industrial area, because I live close to an industrial area, they all came up to the hill. There seems to be more of an understanding of what to do when a big earthquake like this hits. We've had other earthquakes but it hasn't been that big, this is a big one that I felt for the first time in a lot of years here."
