Local authorities initially issued a tsunami warning but lifted it several hours later, and there were no immediate reports of casualties or damage.
The 7.8 magnitude undersea quake struck at a depth of 24 kilometres at about 6:50 pm (1250 GMT), the US Geological Survey said.
The epicentre was several hundred kilometres from the Mentawai Islands, a small chain southwest of the country's main western island of Sumatra.
The quake was felt strongly in Padang, a major city on western Sumatra, sparking panic. An AFP journalist there said people ran from their homes and fled to higher ground by motorbike, car or on foot.
The local BMKG quake-monitoring agency issued a tsunami alert for several provinces with coastlines on western Sumatra but later lifted the warning.
The small Mentawai archipelago is regularly hit by quakes and in 2010 was devastated by a quake-triggered tsunami that left hundreds dead.
Aceh province on the tip of Sumatra was devastated by a quake-triggered tsunami in 2004. The tsunami killed more than 170,000 people in Indonesia and tens of thousands more in other countries around the Indian Ocean.
Disaster agency spokesman Sutopo Purwo Nugroho said tsunami warning sirens were after the earthquake activated and "people responded to the early warning by evacuating to higher places".
"In the Mentawai Islands, there has been no reports of damage and people have been evacuating to higher areas," he told AFP.
Indonesia sits on the Pacific "Ring of Fire", where the meeting of continental plates causes strong seismic activity, and is frequently hit by earthquakes.
Hundreds died when a major quake struck near Padang in 2009.
Plans for evacuation shelters and improved roads to provide better escape routes from tsunamis since 2004 have mostly not been realised, according to experts.
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