The 7.7-magnitude earthquake struck in the Mentawai Islands area west of Sumatra late Monday, generating waves as high as 10 feet that swept away 10 villages, officials said.
One group of Australian tourists reported that their boat with 15 people aboard was destroyed by a "wall of white water" crashing into a bay after the undersea quake.
"We felt a bit of a shake underneath the boat... then within several minutes we heard an almighty roar," said Rick Hallet, an Australian who operates a boat-chartering business in Sumatra.
"I immediately thought of a tsunami and looked out to sea and that's when we saw the wall of white water coming at us," he said.
Arlyno, an official from Indonesia's Disaster Management Agency, told AFP that 23 people were dead and another 167 people had gone missing in the Mentawai islands.
"Ten villages have been swept away by the tsunami," added agency spokesman Agolo Suparto.
Health Ministry Crisis Centre head Mudjiharto, who goes by one name, said the waves reached three yards high and waters swept as far as 600 yards inland on South Pagai island, one of the Mentawai chain.
"Eighty percent of buildings in Muntei village have been damaged by the waves and many people are missing there," Mudjiharto said.
He said medical personnel were on their way to the hardest-hit areas.
Rescuers have launched a search for a boat believed to be carrying a group of nine Australians and a Japanese national that has been missing since the quake.
"We are sending a boat and a chartered plane to search for the boat," said Andrew Judge of SurfAid International.
It was reportedly not equipped with a satellite telephone but SurfAid's Dave Jenkins said its Australian captain had "been around here for a long time. He knew to contact in if he could. So that's why we're extra concerned."
The undersea quake hit at 9:42 pm at a depth of 12.8 miles, south of Padang on Sumatra island, the U.S. Geological Survey said.
"A significant tsunami was generated by this earthquake," said the Pacific Tsunami Warning Centre. The warning was later withdrawn after the danger of further waves had passed.
The first tremor was followed by strong magnitude 6.1 and 6.2 aftershocks several hours later.
Hallet recounted his group's ordeal when the quake struck, with some climbing trees to survive.
"The bay we were in was several hundred metres across and the wall of white water was from one side to the other, it was quite scary," he told Fairfax Radio Network.
Another boat was anchored next to them, he said.
"The wave picked that boat up and brought it towards us and ran straight into us and our boat exploded, caught on fire, we had a fireball on the back deck and right through the saloon within seconds.
"I ordered everyone up to the top deck to get as high as possible, then the boat exploded and we had to abandon ship," he told Australia's Nine Network.
The group jumped into the water, some of them being swept 200 metres inland, and took shelter by climbing trees, waiting for 20 minutes to half an hour until the surges passed.
Eventually all the group were accounted for, he said.
Residents reported shaking as far away as the West Sumatran provincial capital of Padang when the main quake struck.
Indonesia sits on the Pacific "Ring of Fire" where the meeting of continental plates causes high volcanic and seismic activity and the archipelago is frequently struck by powerful earthquakes.
A 7.1-magnitude quake off the north coast of Indonesia's Papua province in June killed 17 people and left thousands homeless.
The 2004 Asian tsunami — triggered by a 9.3-magnitude quake off Sumatra — killed at least 168,000 people in Indonesia alone.
A 7.6-magnitude quake killed about 1,000 people in the port of Padang on September 30 last year.