Hundreds of buildings were flattened and communication lines cut off as the quake, measuring 6.3 on the Richter scale, hit on Tuesday morning.
"So far 70 people were reported dead in various places and scores injured," Sudi Silalahi, a government spokesman, said.
Tremors could be felt as far away as Malaysia and Singapore, 430km from the epicentre, where several buildings were evacuated.
Güncelleme Tarihi: 20 Eylül 2018, 18:16
The tremor hit on Tuesday in a mountainous area about 50km northeast of Padang, a city on Sumatra's western coast, recording a depth of 33km, the US Geological Survey said.
Hospitals were quickly overwhelmed and local officials appealed for urgent help.
The earthquake appeared to have been followed by at least one aftershock almost as strong as the first quake.
Budi Sarwono, the chief of police in Solok, one of the towns affected, had earlier put the toll at 41 but said he expected it to increase.
Many people were trapped in collapsed buildings and there was no official information about the situation at the quake's epicentre because phone lines were down, Utjin Sudiana, West Sumatra's police chief, told AFP."The epicentre is in Batusangkar but communication is disconnected from there so we don't know what the damage is," he added.
"Several houses have collapsed. There are hundreds of victims," Solok mayor Samsurahim told ElShinta radio, adding that a school had been burnt to the ground after the quake.
"We have asked for medical help," he said. "Our facilities here are insufficient."
Doctors were forced to set up outdoors, running drips for the injured and working in hastily erected tents.
Local television showed staff at the main hospital in nearby Padang scrambling in chaos to cope with the wounded.
The Indonesian archipelago sits on the Pacific Ring of Fire where continental plates meet, causing frequent seismic and volcanic activity.