The flooding has left about 10,000 people homeless in Honiara alone.
The US Geological Survey reported the quake was centred about 30km west of the city of Kirakira, at a depth of 63km.
It believed the likelihood of casualties and damage was low.
At least seven have been killed in floods in the Solomon Islands, making it one of the Pacific's worst disasters of recent times.
About 30 people are believed to be missing, and there have been reports of children's bodies floating down the main river in the Solomons' capital of Honiara.
The floods, from a slow-moving tropical depression threatening last night to turn into a cyclone, have also left more than 10,000 people temporarily homeless in Honiara alone.
They are clustering in 16 evacuation centres in local schools on high ground in the city of 70,000 people, where the police have also been rounding up looters.
Aid workers fear outbreaks of diseases from polluted water.
An old bridge through Honiara's Chinatown has been swept away, carrying a young mother and her baby daughter with it, said the Solomon Times, quoting a witness to the collapse.
See the article here:
Quake hits flooded Solomon Islands
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