Eyewitnesses said they had fled their lives when houses were swept along the beach in the churning sea.
The bassist and manager of the band was killed, said singer Riefian Fajarsyah in a video posted on Instagram. Three other members of Seventeen and Fajarsyah's wife, whose birthday is Sunday, are still missing, he said.
According to Sutopo Purwo Nugroho, head of public relations for the Indonesian National Disaster Mitigation Agency, 843 people were injured and another 28 people are unknown.
At least 558 houses were destroyed, nine hotels, 60 restaurants and 350 boats were badly damaged. This is an indication of the impact of the tsunami on residential and tourist areas.
Until Sunday afternoon, no foreigners had been killed or injured.
Tsunami caused by underwater landslides
It is believed that the tsunami was triggered when the volcano Krakatoa erupted in the Sunda Strait between the islands of Java and Sumatra and triggered a series of underwater landslides Geological Agency (BMKG).
As the displaced rock moved beneath the surface of the water, it "squeezed" the water, CNN meteorologist Allison Chinchar said, producing the tsunami.
Krakatoa lies between the islands of Java and Sumatra.
The effects of the tsunami were amplified by a tsunami caused by the full moon, BMKG said in a press release.
Krakatoa is known for its eruption in 1883, one of the deadliest in history, when more than 36,000 people were killed.
Despite the devastating 2004 tsunami, which killed hundreds of thousands of people, Indonesia lacks adequate equipment to warn of a tsunami threat.
"We need an early-warning system with multiple threats," Nugroho said. "And we need a lot of it."
Nugroho pointed out that tsunamis are faster and less predictable than tidal waves caused by atmospheric conditions.
"We used to know that a tsunami happened after an earthquake, there was no quake last night," he said, referring to the underground landslides. "That's why there was no warning."
Prayers pour in from all over the world
Pope Francis prayed for the tsunami victims at his regular Sunday Angelus service in St. Peter's Square.
"I stand with the exiles and all concerned in God for relief in their suffering," he said. "I appeal that these brothers and sisters do not lack our solidarity and the support of the international community."
The International Federation of Red Cross and Red Crescent Societies in Indonesia expects the death toll to rise, spokeswoman Kathy Mueller said. It will help you bring essential household items, clean water and equipment to remove debris.
According to WFP spokeswoman Bettina Luescher, the United Nations World Food Program also agreed to support the Indonesian government.
Jamaluddin Masrur and Yosef Riadi of CNN reported from Jakarata, Indonesia, NIcola Ruotolo from Rome. CNN's Steve Almasy, Nicole Chavez and Jaide Timm-Garcia have contributed to this report.