The 7.9-magnitude undersea quake struck at a depth of 10 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 island chain southwest of the country's main western island of Sumatra.
The local BMKG quake-monitoring agency issued a tsunami alert for parts of Sumatra, including West Sumatra, North Sumatra, Aceh, Bengkulu and Lampung.
The closest major city on Sumatra was Padang. An AFP journalist there said people ran out of their homes to higher ground.
However the USGS said there was a "low likelihood of casualties and damage".
"There are likely to be no affected structures in this region," it added on its website.
Indonesia sits on the Pacific "Ring of Fire", where the meeting of continental plates causes strong seismic activity, and is frequently hit by earthquakes.
A huge undersea earthquake in the Indian Ocean in 2004 triggered a tsunami that engulfed parts of Aceh.
The tsunami killed more than 170,000 people in Indonesia and tens of thousands more in other countries around the Indian Ocean.
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