The U.S. Geological Survey said the strongest quake had a magnitude of 7.5 and was centered at a depth of 6 miles (10 kilometers) about 35 miles (56 kilometers) northeast of the central Sulawesi town of Donggala. It briefly triggered a tsunami warning.
An official with the local disaster agency, Akris, said "many houses have collapsed."
"It happened while we still have difficulties in collecting data from nine villages affected by the first quake," he told The Associated Press. "People ran out in panic."
Television footage showed people running into the streets. Woman and children wailed hysterically in a video distributed by the National Disaster Mitigation Agency, which also released a photo showing a heavily damaged department store.
Disaster agency spokesman Sutopo Purwo Nugroho said communications with the region are disrupted.
He said in a statement there is "much damage" in the Donggala area, which is home to about 300,000 people.
A swarm of strong aftershocks including one of magnitude 6.7 shook the region.
"People are encouraged to remain vigilant," Sutopo said. "It is better not to be in a house or building because the potential for aftershocks can be dangerous. People are encouraged to gather in safe areas. Avoid the slopes of hills."
The airport in Central Sulawesi province's capital, Palu, halted operations for 24 hours due to damage, according to a notice from AirNav, which oversees airline traffic in Indonesia.
Donggala was hit earlier Friday by a magnitude 6.1 earthquake that based on preliminary information killed one person, injured 10 and damaged dozens of houses.
"All the things in my house were swaying and the quake left a small crack on my wall," Donggala resident Mohammad Fikri said by telephone.
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 magnitude 9.1 earthquake off Sumatra in western Indonesia triggered a tsunami that killed 230,000 people in a dozen countries.