Hundreds of buildings were destroyed by the wave, which hit the coast of southern Sumatra and the western tip of Java about 9.30 pm (1430 GMT) following the eruption of a volcano known as the "child" of the legendary Krakatoa, national disaster agency spokesman Sutopo Purwo Nugroho said.
Search and rescue teams were scouring rubble for survivors, with at least 584 people injured and twenty reported missing across three regions.
Images broadcast on television showed the wave pushed a tangled mess of corrugated steel roofing, timber, rubble and flotsam inland from the coast at Carita beach, a popular day-tripping spot on the west coast of Java.
Elsewhere it uprooted trees and left a trail of debris strewn across the ground.
Muhammad Bintang, who was at Carita beach when the wave hit, described a sudden surge of water that plunged the tourist spot into darkness.
"We arrived at 9pm for our holiday and suddenly the water came -- it went dark, the electricity is off," the 15-year-old told AFP.
"It's messy outside and we still cannot access the road."
In Lampung province, on the other side of the strait, Lutfi Al Rasyid said he fled the beach in Kalianda city in fear for his life.
"I could not start my motorbike so I left it and I ran... I just prayed and ran as far as I could," the 23-year-old told AFP.