There have been no immediate reports of damage.
The USGS said the earthquake struck at 19:49 local time (12:49 GMT). It said the epicentre was 808km (502 miles) southwest of the city of Padang, and 10km deep.
Indonesian officials issused a tsunami warning for the regions of West Sumatra, North Sumatra and Aceh.
Australia also issued a tsunami warning for Cocos Island and Christmas Island, in the Pacific and put a watch in place for the western Australian coast, including the city of Perth.
The earthquake was felt strongly in Padang for a few seconds, AFP reports, with people running out of their homes to higher ground.
Traffic ground to a halt and there was a sense of panic on the streets.
In 2004 an 8.9 magnitude earthquake triggered the world's deadliest ever tsunami, killing more than 200,000 people.
After that disaster, a more effective tsunami monitoring system was put in place. Warnings are now issued more frequently after earthquakes in the area.