The western edge of the Solomons archipelago has been battered by waves up to five meters high.
The town of Gizo has been badly damaged. It was about 45 kilometers from the epicenter of the underwater earthquake.
Residents have told how buildings on the seafront were destroyed as the wall of water came crashing through at just after 7:40 in the morning.
Some reports have said that entire villages have been washed away. The extent of the damage in this remote part of the Solomon Islands may take days to emerge. Charles Stennett from the Solomon Islands Broadcasting Corporation says Gizo was hit hard.
"As it went through the town it went about 50 to 70 meters inland and most of the buildings especially government offices and private offices and shopping and resort accommodation for tourists were flooded this morning."
The emergency sparked fear across the region.
The capital Honiara was rocked by tremors that lasted for up to two minutes although little damage has been reported. A tsunami alert was issued to parts of Indonesia, Papua New Guinea and Australia, although it was cancelled about five hours after the quake.
Australian officials closed some east coast beaches and suspended ferry services as a precaution.
Pupils at some low-lying schools were also sent home amid fears of dangerous waves and flooding. Residents in some coastal areas packed their cars with supplies and headed to higher ground.
The authorities have said that the threat to Australia has now receded. In the Solomon Islands the search for survivors is under way. In Gizo, many people are homeless and supplies of food and water are scarce.
The Solomon Islands is an archipelago of more than 200 islands northeast of Australia. About half a million people live on the islands, which lie on the Pacific Basin's "Ring of Fire," an arc of volcanos and fault lines where earthquakes are frequent.