People living hundreds of kilometers from the epicenter reported feeling the massive shake, which came hours after a smaller jolt killed at least one person in the same part of the country.
The natural disasters in July and August killed almost 500 people on the holiday island, hundreds of kilometres southwest of Sulawesi.
Just 3 hours before the natural disaster, the same area was hit by a smaller quake that measured 6.1, killing at least one person and injuring 10 others. The water smashed into buildings and the damaged mosque.
The huge tremor earlier destroyed buildings and sent panicked residents fleeing into the streets.
Palu resident Morits Kodongan told the Jakarta-based private television network Metro TV that "residents need gasoline because it has started to run out".
The military, national police, search and rescue agency have dispatched personnel to search for missing people and support evacuees.
She said a tsunami warning triggered by the biggest quake was in place for about half an hour and was lifted after the tsunami was over.
An image released by the Indonesian National Board for Disaster Management (BNPB) shows a collapsed shopping mall after a 7.7 magnitude quake that struck Donggala, Central Sulawesi on Friday. It was followed by at least two dozen aftershocks.
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"A tsunami has happened in Palu", said Rahmat Triyono, head of the agency's natural disaster and tsunami division, referring to the city of 350,000 almost 80 kilometres from the quake's epicentre. "There is a ship washed ashore".
"Everyone was getting out their homes, shouting in fear".
Indonesia is prone to earthquakes because it lies on the Ring of Fire - the line of frequent quakes and volcanic eruptions that circles virtually the entire Pacific rim. "The tsunami also damaged scores of houses", an official told Xinhua news agency over telephone.
In December 2004, a massive magnitude 9.1 quake off Sumatra in western Indonesia triggered a tsunami that killed 230,000 people in a dozen countries.
"Most people killed were due to the tsunami because most of dead bodies were found on Talise beach on Palu Bay", Sutopo said.
Indonesia's Aceh province was the hardest hit area, but the tsunami affected coastal areas as far away as Africa.
This latest 7.7-magnitude tremor on the Indonesian island of Sulawesi initially sparked an early tsunami warning as people were urged to evacuate to higher ground.