The US Geological Survey said the 7.4 earthquake was shallow, only 35 kilometres below the seabed and centred 111 kilometres south of Kira Kira, on the island of Makira.
It said the likelihood of casualties or damage from the quake was low.
A tsunami warning was issued for Solomon Islands, Vanuatu and Papua New Guinea by the Pacific Tsunami Warning Centre, but it later cancelled the alert for all three areas.
It was the second powerful earthquake to hit the Solomons in less than 24 hours.
Another major quake measuring 7.6 struck in a similar area on Sunday morning, 100 kilometres south of Kira Kira.
Oxfam Solomon Islands director Katie Greenwood said there were reports that one person died after they first earthquake as they were trying to go to higher ground, and reports of minor damage.
Graham Kenna, from Save the Children in the capital Honiara, said the earlier quake on Sunday was the worst one he had felt for some time.
“I was counting it – that’s what we do when we get earthquakes here – and it was for 25 seconds,” he said.
“The initial reports were that it was going to be an 8.3 earthquake, so panic set in in the displaced camps where we have all these people that have just been rescued from the flood.”
Kenna said there was a small tsunami in Santa Ana, close to the epicentre.
Greenwood said Solomon Islanders are resilient but the natural disasters have taken a toll.
“There have been in fact 36 earthquakes and tremors and aftershocks over that last 24 hour period and with what has already happened it does certainly take its psychological toll.”
Solomon Islands police say they will be checking isolated areas in the country for damage.
Tens of thousands are still homeless from floods last week which washed away homes and bridges in Honiara.
There are still 50,000 to 60,000 people homeless – most without shelter and fresh water.
Various camps have been set up in schools around Honiara and Guadalcanal. Many are uncertain as to where they will return as most have lost their homes and belongings, destroyed by the floods.
A total of 21 people were killed in the floods that swept through the capital and elsewhere on the main island of Guadalcanal as well as Isabel Province. At least two people are still missing.
Major roads throughout Guadalcanal are ruined and bridges have collapsed, making it hard for emergency teams to assess the damage. – ABC