Another 165 have been injured.
The area is known for its earthquakes and tsunamis.
The Indonesian Meteorology, Climatology, and Geophysical Agency (BMKG) said the wave was not caused by an earthquake but was possibly the result of volcanic activity at Anak Krakatoa (child of Mount Krakatoa).
Video filmed at one of the affected beaches and posted on Twitter shows the wave rolling in as beachgoers scramble away from the water.
READ MORE: Earthquakes today: Indonesia HAMMERED by 6.2 tremors
Of the video, Sutopo Purwo Nugroho, an Indonesian civil servant and head of public relations at the Indonesian National Board for Disaster Management said in a tweet: “The footage shows the impact of the tide on the coast of Anyer Pandeglang Regency South Lampung, which left one person dead and 11 people injured.
“The wounded were treated in hospital.”
Mr Nugroho speculated the “cause of the tsunami in Pandeglang and South Lampung is possibly a combination of underwater landslides due to the influence of the eruption of Anak Krakatoa (child of Mount Krakatoa) and the high tides caused by the full moon”.
He added work was still being done to confirm the cause of the disaster.
READ MORE: Indonesia earthquake: Huge 6.1 magnitude quake rocks Ring of Fire
The death toll from the disaster is likely to rise, Mr Nugroho warned.
More video images on Twitter show cars and entire residential roads submerged by sea water.
According to a statement from the Meteorology, Climatology and Geophysics Agency (BMKG), “the tsunami hit several areas of the Sunda Strait, including beaches in Pandeglang regency, Serang, and South Lampung”.
The tsunami struck at roughly 9.30pm local time on Saturday night (2.30pm GMT), it said.
Endan Permana, head of the National Disaster Mitigation Agency in Pandeglang, told Metro TV police were providing immediate assistance to victims in Tanjung Lesung in Banten province, a popular tourist getaway not far from Jakarta, as emergency workers had not arrived in the area yet.
Mr Permana said: “Many are missing.”
The deaths from the tsunami were reported in the Pandeglang, South Lampung and Serang regions.
Emergency officials are now investigating whether the tsunami was caused by Anak Krakatoa, a volcanic island in the Sunda Strait.
In September, more than 2,000 people died when a powerful earthquake struck just off the central Indonesian island of Sulawesi, setting off a tsunami that swamped the coastal city of Palu.
The area is prone to huge seismic disasters because it lies in the volatile Ring of Fire – a horseshoe shape of frequent quakes and volcanic eruptions that snakes around almost the entire Pacific Rim.
Anak Krakatoa has experienced a surge of activity in recent months.
Indonesia’s geologic agency said the volcano erupted for two minutes and 12 seconds on Friday, creating an ash cloud that rose 400 metres (1,300ft) above the mountain.
It recommended that no-one be allowed within two kilometres of the crater.