The epicentre of the 7.6-magnitude quake was about 50km (30 miles) off the coast of the Indonesian island, near the city of Padang.
There are reports of widespread destruction to buildings and bridges.
It comes hours after a tsunami triggered by a separate South Pacific quake killed more than 100 people.
A tsunami watch issued by the Pacific Tsunami Warning Center in the wake of the Indonesian quake has been lifted.
Aid "on the Way"
At least six disaster management teams are on their way to the city of Padang. We`ve been told it will take up to 10 hours to get to the areas most affected.
Vice-President Jusuf Kalla said the death toll was likely to continue to rise sharply, as so many buildings including schools, shops and hotels had collapsed.
Rustam Pakaya, head of the health ministry`s crisis centre, said a hospital was among the collapsed buildings.
At least six rescue teams were on their way to Padang, capital of West Sumatra province, from neighbouring provinces, he said, but would not arrive for at least 10 hours.
Local media reported the roof of the city`s airport had also collapsed.
Mukhlis Rahman, mayor of the Pariaman District, one of the worst hit areas, said the weather was hindering efforts to clear up after the disaster.
"The quake was followed by a very heavy rain. Many houses and some building are flattened in my area. But I cannot yet verify too much. We will try to compile the data and distribute aid once the rain subsides," he told the BBC.
Witnesses said residents ran out of buildings in Padang - which has a population of 900,000, and surrounding cities.
"A number of hotels in Padang have been destroyed," Rahmat Triyono, from the Indonesian geophysics and mete