Waves of up to two metres (6.6ft) high swept through the city of Palu on Sulawesi island after the magnitude 7.5 quake brought down several buildings and sent people fleeing from their homes.
Many of those killed were at a beach festival in Palu, the capital of Central Sulawesi province, which was strewn with debris from collapsed buildings and pooled seawater.
“When the (tsunami) threat arose yesterday, people were still doing their activities on the beach and did not immediately run and they became victims,” disaster agency official Sutopo Purwo Nugroho said.
A magnitude 6.1 earthquake which earlier hit central Sulawesi also reportedly killed one person and injured 10 others, as well as damaging dozens of houses.
Authorities are struggling to co-ordinate the rescue effort because a power outage has cut communications around Palu and the nearby town of Donggala, which is closest to the epicentre of the quake.
Officials said some victims had been trapped in the rubble of collapsed buildings.
Mr Nugroho said: “Bodies of victims were found in several places, because they were hit by the rubble of collapsing buildings or swept by tsunami… but we are still collecting data.”
Indonesian president Joko Widodo said the military was being called into the disaster-struck region to help search-and-rescue teams reach victims.
The earthquake hit at a depth of 10km (6.2 miles) just before 6pm local time (12pm UK time) on Friday, the US Geological Survey said.
A tsunami warning was issued but lifted within the hour.
Footage posted online showed waves of water bring down several buildings and swamp a large mosque in Palu.
“I just ran when I saw the waves hitting homes on the coastline,” said Palu resident Rusidanto.
More than 600,000 people live in Donggala and Palu.
The 7.5 magnitude tremor later on was more powerful than a series of quakes that killed hundreds on the Indonesian island of Lombok in July and August.
Indonesia is prone to earthquakes because of its location on the Ring Of Fire, an arc of volcanoes and fault lines in the Pacific Basin.
In December 2004, a massive 9.1 magnitude earthquake off Sumatra in western Indonesia triggered a tsunami that killed 230,000 people in a dozen countries.
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