Hundreds of homes and other buildings were "heavily damaged" when the tsunami struck along the rim of the Sunda Strait late on Saturday, Sutopo Purwo Nugroho, spokesman for the disaster mitigation agency, said.
Thousands of residents were forced to evacuate to higher ground. There was no estimate on the number of missing.
TV images showed the seconds when the tsunami hit the beach and residential areas in Pandeglang on Java island, dragging with it victims, debris, and large chunks of wood and metal.
On December 26 in 2004, an Indian Ocean tsunami triggered by an earthquake killed 226,000 people in 13 countries, including more than 120,000 in Indonesia.
The eruption of Krakatau in 1883 killed more than 36,000 people in a series of tsunamis. Anak Krakatau is the island that emerged from the area once occupied by Krakatau, which was destroyed in 1883. It first appeared in 1927 and has been growing ever since.
Saturday's tsunami was the latest in a series of tragedies that have struck Indonesia, a vast archipelago, this year. Successive earthquakes flattened parts of the tourist island of Lombok, and a double quake-and-tsunami killed thousands on Sulawesi island. Nearly 200 people died when a Lion Air passenger plane crashed into the Java Sea in October.
Authorities warned residents and tourists in coastal areas around the Sunda Strait to stay away from beaches and a high-tide warning remained in place through till Dec. 25.
"Those who have evacuated, please do not return yet," said Rahmat Triyono, an official at the Meteorology, Climatology and Geophysics Agency (BMKG).
President Joko Widodo, who is running for re-election in April, said on Twitter that he had "ordered all relevant government agencies to immediately take emergency response steps, find victims and care for the injured".
Vice President Jusuf Kalla told a news conference the death toll would "likely increase".
Rescue workers and ambulances were finding it difficult to reach affected areas because some roads were blocked by debris from damaged houses, overturned cars and fallen trees.