The magnitude-8 quake triggered tsunami warnings throughout the South Pacific and as far north as Hawaii, though officials canceled the alert after the danger period passed.
Police and residents said a wave several meters (yards) high crashed ashore at Gizo, a regional center in the country's west, inundating buildings and causing widespread destruction.
"All the houses near the sea were flattened," as water "right up to your head" swept through the town, resident Judith Kennedy told The Associated Press by telephone.
"The downtown area is a very big mess from the tsunami and the earthquake," she said. "A lot of houses have collapsed. The whole town is still shaking," from aftershocks.
Another witness, Harry Wickham, who owns a waterfront hotel in Gozi, said the damage was widespread.
"The waves came up probably about 10 feet (3 meters) and swept through town," he told Australia's Nine Network television by telephone. "There's a lot of water damage and a lot of debris floating around.
"Ten feet of water washing through town - you can imagine what damage it has done here."
Another town in the west, Munda, was also believed to be badly damaged, officials and the national broadcaster said, but communications were difficult and details were not confirmed.
The U.S. Geological Center said the magnitude 7.6 earthquake struck about 10 kilometers (6 miles) beneath the sea floor about 350 kilometers (215 miles) northwest of the Solomons capital of Honiara at 7:39 a.m. (20:39 GMT Sunday). It later upgraded the strength to magnitude to 8.0.
The Hawaii-based Pacific Tsunami Warning Center reported the quake at magnitude 8.1, and said an earthquake of that strength could cause a destructive tsunami and issued a warning bulletin for the Solomon Islands and neighboring Papua New Guinea.
It ordered a a lower-level "tsunami watch" for other places, including most South Pacific countries, but later canceled the alert.
The center said a 15-centimeter (6-inch) wave had been reported in Honiara, the capital.
Police Sgt. Godfrey Abiah said in Honiara that police in Gizo had received warning about a possible tsunami and were helping people leave the town for higher ground when the wave hit.
"We have lost radio contact with the two police stations down there and we're not getting any clear picture from down there," he told The Associated Press by telephone.
A spokesman for Prime Minister Manasseh Sogavare, Deli Oso, said the quake was felt in Honiara but no damage was done.
The Australian Bureau of Meteorology also set the earthquake's magnitude at 8.1, but said it had detected no tsunami threat for Australia's northeast coast.
"At this stage, the warning remains current but we have not detected anything abnormal," said spokesman Peter Jarrott.