Tuesday's quake, which measured a magnitude of 6.4 and was followed by an aftershock of 6.0, struck near the city of Padang on Sumatra's west coast.
Al Jazeera correspondent Hamish MacDonald, who is in Padang, said the quake sparked widespread fears that a tsunami might follow, in a repeat of the December 2004 disaster that left tens of thousands dead.
Although there was no tsunami, the quake was powerful enough to be felt in neighbouring Singapore and Malaysia, where many buildings were evacuated.
The worst hit area was around the town of Solok, closest to the epicentre of the quake.
Locals there said they were used to frequent tremors, but had felt nothing as strong as Tuesday's quake in recent memory.
Many people were killed by falling masonry or were trapped in buildings by fires caused by the quake.
Some survivors spent the night in tents outside their homes or in open fields, but many had little or no shelter.
"I was cold last night because I only slept on a mat, I did not have a tent. I am afraid there will be another quake," Soni Safmiwati, a 32-year-old mother of two, told Reuters.
Officials say that casualty figures are likely to rise because many people were still trapped and the rescue process would have to be done manually as heavy machinery cannot reach some districts.
Hospitals in some areas said they had been overwhelmed with injured, with many patients treated outside because of fears of further quakes.
| The powerful quake killed at least 70 people [AFP]|
Susilo Bambang Yudhoyono, the Indonesian president, who was scheduled to visit Medan in North Sumatra, is instead expected to visit the area around Solok on Wednesday.
Meanwhile, the government and the Red Cross have begun distributing supplies such as cooking oil, rice, tents, medicine and drinking water.
United Nations aid agencies said a team of health, sanitation and nutrition experts would arrive in the affected area "on the first available flight" to assess the situation.
Earthquakes are frequent in Indonesia, the world's fourth most populous country.
Its 17,000 islands lie along a belt of intense volcanic and seismic activity, part of what is called the "Pacific Ring of Fire".
In December 2004 a quake in the Indian ocean off Sumatra and the tsunami it caused left about 170,000 people dead or missing in northern Aceh province.