The tsunami followed an eruption late Saturday from the Anak Krakatoa volcano, according to the country's national disaster agency.
Authorities say rescue equipment is being sent to badly hit areas following the waves that hit during the night without warning.
At least 745 people have been injured and the death toll is expected to rise.
The wave hit the coast of southern Sumatra and the western tip of Java at about 9:30 pm (1430 GMT), destroying hundreds of buildings and sparking mass panic.
Rescue operations under way
Search and rescue teams are scouring rubble for survivors. At least 30 people are reported missing across three regions.
Heavy equipment was being transported to some of the worst-hit areas to help search for victims, according to Indonesia's geological agency. Evacuation posts and public kitchens have also been set up for evacuees.
Abu Salim, a member of the Tagana disaster volunteer group, said he helped evacuate victims in Banten province.
"We evacuated the victims who (...) were injured, we took them to health clinics. Most of them suffered from broken bones," he said, adding that he feared more were missing.
Scenes of havoc on social media
Images of the aftermath of the tsunami in coastal areas showed a trail of uprooted trees and debris strewn across beaches. A tangled mess of corrugated steel roofing, timber and rubble was dragged inland at Carita beach, a popular day-trip spot on Java's west coast.
Video of local pop group Seventeen being swept away by the tsunami
Last night, when Indonesian band called Seventeen was on the stage in Tanjung Lesung Beach, Anyer, Indonesia, a massive wave hit them from behind the stage. The bassist and the road manager are reported dead, other members still missing.#PrayForAnyerpic.twitter.com/XsRfWGfFGpI Tried to Work (@ButYoongiFlexed) 23 décembre 2018
Witnesses have reported cars and containers being dragged along by the water, while electric poles and trees tumbled to the ground
The eruption of Krakatoa's 'child'
The tsunami followed the eruption of a volcano popularly known as the "child" of Krakatoa, the volcano that famously exploded in 1883, killing more than 30,000 people.
Anak Krakatoa emerged in the Sunda Strait between Java and Sumatra nearly half a century after Krakatoa.
A new moon on Saturday coincided with Anak Krakatoa's eruption, which reportedly caused an abnormal tidal surge and an underwater landslide, which may have provoked the tsunami, according to officials.
Anak Krakatoa had been showing signs of heightened activity for days, spewing plumes of ash thousands of metres into the air.
Although relatively rare, submarine volcanic eruptions can cause tsunamis due to the sudden displacement of water or slope failure, according to the International Tsunami Information Centre.