Solomons officials reported two 4 foot, 11-inch waves hit the western side of Santa Cruz Island, damaging between 70 and 80 homes and properties, said George Herming, a spokesman for the prime minister. Many villagers had headed to higher ground as a precaution, Herming said.
Solomon Islands Police Commissioner John Lansley said local police patrols reported that several people were presumed dead, though the reports were still being verified.
"Sadly, we believe some people have lost their lives," he said. "At the moment we potentially know of four, but there may of course be more."
One of the people presumed dead was fishing in a dugout canoe when the first wave hit, sweeping him out to sea, Herming said. Officials were searching for his body. Another woman was believed to have drowned when the water rushed into her village, Herming said.
Four villages on Santa Cruz were hit by the waves, with two facing severe damage, Lansley said. Other areas of the Solomons did not appear to have been seriously affected.
Disaster officials were struggling to reach the remote area after the tsunami flooded the airstrip at the nearest airport and left it littered with debris.
The tsunami formed after a magnitude-8.0 earthquake struck near the town of Lata, on Santa Cruz in Temotu, the easternmost province in the Solomons, about a 3-hour flight from the capital, Honiara. Temotu has a population of around 30,000.
The Pacific Tsunami Warning Center said a tsunami of about 3 feet was measured in Lata wharf. Smaller waves were recorded in Vanuatu and New Caledonia.
The center canceled warnings for tsunami waves further away.