Solomons officials reported two 1.5-meter (4 foot, 11-inch) waves hit the western side of Santa Cruz Island, damaging around 50 homes and properties, said George Herming, a spokesman for the prime minister. There were no reports of injuries or deaths. Villagers were heading for higher ground as a precaution, Herming said.
The tsunami formed after an 8.0-magnitude earthquake near Lata on Santa Cruz in Temotu province, the easternmost province of the Solomons, about a 3-hour flight from the capital, Honiara. The region has a population of around 30,000 people.
The Pacific Tsunami Warning Center said a tsunami of about a meter (3 feet) was measured in Lata wharf, in the Solomon Islands. The center said an 11-centimeter (4.3-inch) wave was observed in neighboring Vanuatu.
The center cancelled earlier warnings for tsunami waves further away.
In Honiara, the warnings had prompted residents to flee for higher ground.
"People are still standing on the hills outside of Honiara just looking out over the water, trying to observe if there is a wave coming in," said Herming. So far, he had received no reports that a wave had been spotted in Honiara.
Atenia Tahu, who works for the Solomon Islands Broadcasting Corp. in Honiara, said most people were remaining calm.
"People around the coast and in the capital are ringing in and trying to get information from us and the National Disaster Office and are slowly moving up to higher ground," Tahu said. "But panic? No, no, no, people are not panicking."
An official at the disaster management office in Vanuatu said there were no reports of damage or injuries there.
More than 50 people were killed and thousands lost their homes in April 2007 when a magnitude 8.1 quake hit the western Solomon Islands, sending waves crashing into coastal villages.
The Solomons comprise more than 200 islands with a population of about 552,000 people. They lie on the "Ring of Fire" - an arc of earthquake and volcanic zones that stretches around the Pacific Rim and where about 90 percent of the world's quakes occur.
The U.S. Geological Survey said the quake struck 81 kilometers (50 miles) west of Lata, at a depth of 5.8 kilometers (3.6 miles). The warning area does not include Hawaii and North and South America.