Many residents in Padang, West Sumatra, fled to higher ground after the earthquake
Scores of houses were destroyed by waves after the 7.7 magnitude quake, which struck 13 miles (20km) under the ocean floor near the Mentawai islands.
Ten villages on the islands were swept away by the tsunami, a disaster official told the AFP news agency.
Australian officials are trying to contact a group of missing surfers.
The group of between eight and 10 missing Australians was on a surfing charter boat in the area, which is a popular surfing destination reached only by boat.
The search and rescue operation is being seriously hampered by bad weather, officials have told the BBC's Karishma Vaswani in Jakarta.
Heavy rain is preventing helicopters from accessing the area and boats cannot reach the islands either, because the dock on the island of South Pagai has been completely destroyed.
Children 'swept away'
There is no tsunami warning system in place around the Mentawai islands, and initial reports about whether a tsunami had actually been generated were confused.
Multiple eyewitnesses say a huge wave was created by the quake, which seriously damaged villages or even washed them away entirely.
The islands of South Pagai and North Pagai were reported to be particularly badly affected.
He said 200 body bags were being sent to the region in case they were needed.
"Ten villages have been swept away by the tsunami," National Disaster Management Agency spokesman Agolo Suparto told AFP.
Most buildings in the South Pagai coastal village of Betu Monga were destroyed, Hardimansyah, an official with the regional branch of the Department of Fisheries, told the Reuters news agency by phone.
"Of the 200 people living in that village, only 40 have been found. 160 are still missing, mostly women and children," he said.
"We have people reporting to the security post here that they could not hold onto their children, that they were swept away. A lot of people are crying."
Heri Suprapto, the head of Kepuhargo village in the Mentawai islands, told the BBC's Indonesia service that 372 "very weak" people from three villages had been evacuated.
"Transportation has also been prepared for villagers who are in good health whenever evacuation needs to be done. Preparations are also under way to evacuate individuals by using motorbike and small cars."
'Wall of white water'
Rescue workers are preparing to evacuate victims from quake-hit areas
The Southern Cross was carrying up to 10 people - Australia's AAP news agency said nine Australians and a Japanese man had been on board.
SurfAid, a charity which supports villages in the Mentawai islands, said the boat's skipper was experienced and knew the area well.
"He knew to contact in if he could. So that's why we're extra concerned," said the charity's founder, Dave Jenkins.
Meanwhile, another group of Australians said their boat was destroyed by a wall of water.
Captain Rick Hallet told Australian media that his boat was anchored off the shore when the waves came.
"We felt a bit of a shake underneath the boat... then within several minutes, we heard an almighty roar," he said.
"I immediately thought of a tsunami and looked out to sea and that's when we saw the wall of white water coming at us," he said.
The wave brought another boat crashing into them and sparked a fire, forcing them to jump into the sea.
Some of those on board were swept up to 200m inland by the wave, he said.
