People throughout the Pacific island chain awoke to a strong quake at 7:14 am, government spokesman George Herming said. People on Makira and nearby islands southeast of the capital, Honiara, reported seeing three large waves after that temblor, he said.
The magnitude-7.6 quake's epicenter was 323 kilometres southeast of Honiara, at a depth of 29 kilometres, according to the US Geological Survey.
Following the morning quake, the Pacific Tsunami Warning Center canceled a tsunami warning after issuing an alert for some Pacific islands. The centre reported that sea level readings indicated a small tsunami was generated that may have caused some destruction near the epicenter.
Late Sunday night, a magnitude-7.5 quake struck in the same area at a depth of 35 kilometers, the USGS said.
The Solomon Islands, home to 600,000 people, was already reeling from devastating flash floods that struck Honiara and other areas April 3. The floods have killed 23 people and left 9,000 more homeless. Herming said up to 30 more people remain missing.
"It has really been a tough time," he said.
Andrew Catford, the Solomon Islands country director for World Vision, said after the morning quake that the aid group's staff in the Kirakira office in Makira province reported that there was no tsunami, but strong currents and heavy waves pounding the reefs. He said the group's staff evacuated to higher ground as a precaution.
"We felt this one strongly in Honiara. It was close to 30 seconds long," he said.
Following the first quake, the Pacific Tsunami Warning Center issued a warning for the Solomon Islands, Vanuatu and Papua New Guinea.
US officials said there was no threat of a tsunami to the coasts of California, Oregon, Washington state, Hawaii or Alaska. Paul Whitmore, director of the National Tsunami Warning Center in Alaska, said powerful waves posed no threat to the US West Coast or Canada after the quake.
The Solomon Islands lies on the "Ring of Fire", an arc of earthquake and volcanic activity that stretches around the Pacific Rim.