The epicentre of the quake, which struck at 3 am (2000 GMT Monday), was in the sea near the Mentawai islands at a depth of 15.5 kilometres (more than 9 miles), the United States Geological Survey said.
No casualties or severe damage were reported.
"The quake was so strong that we struggled to stand up and walk outside. We were struggling to get out of the house, we had to hold on to the walls," said Patriz Sanene, a 34-year-old resident of Siberut, Mentawai's largest island.
"This is the strongest quake... this year. I thought probably there will be a tsunami. Thank God there is no tsunami."
Indonesia's geophysics agency (BMKG) issued a tsunami warning that lasted around two hours after initially reporting a higher quake magnitude of 7.3.
BMKG chief Daryono, who like many Indonesians goes by one name, told residents "in the potential tsunami region to remain calm and avoid the shore".
There were several aftershocks, he added.
Residents said they were jolted awake by the shaking, and rushed outside.
Sudarmono Siribere, 35, said he and his family "had to brave the pouring rain to go to higher ground".
Footage shared with reporters by the local BNPB rescue agency showed residents holding umbrellas and wearing raincoats as they fled on foot and on scooters.
Officials said the quake was also felt in the coastal city of Padang in western Sumatra, which is around 200 km from the epicentre.
Indonesia experiences frequent earthquakes due to its position on the Pacific "Ring of Fire", an arc of intense seismic activity where tectonic plates collide.
In 2004, a 9.1-magnitude quake struck Aceh province on Sumatra island, causing a tsunami and killing more than 170,000 people in Indonesia.
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