The quake, which measured 7.8 in magnitude, hit around 70km from the township of Kirakira, the US Geological Survey reported.
It occurred at 04:40 local time on Friday (December 9) and was followed by a series of aftershocks.
Phone lines and electricity power sources went down in areas of the island.
There were no accounts of casualties, BBC News reports.
In the island of Malaita, close to the quake’s epicentre, there were reports of damage to buildings although the extent of the destruction was currently unknown, Loti Yates director for the Solomon Islands National Disaster Management Office told Reuters.