Mount Rokatenda, on the island of Palue, sent huge clouds of red-hot ash and rocks two kilometres (1.2 miles) into the air, said vulcanology centre head Surono.
"There are six victims who were engulfed in hot lava," Johanes Berchmans, head of the disaster management agency in Sikka district, told AFP.
"They were swept away by hot lava when they were asleep on Punge beach."
Three adults aged between 58 and 69 were found dead while three children aged between five and eight were also killed, though their bodies had not yet been recovered, he said.
Rokatenda has been showing signs of increased volcanic activity since October, with authorities banning people from any activities within three kilometres of its crater.
Some 2,000 people had previously been evacuated from the island due to the volcanic activity leaving around 8,000 before today's eruption, said Berchmans.
"Tomorrow our staff will go from area to area to pick up anyone willing to leave the island," he told AFP.
The volcano began erupting at 04:27 am (2027 GMT yesterday) and it continued for nearly four hours, said Surono.
Indonesia has dozens of active volcanoes and straddles major tectonic fault lines known as the "Ring of Fire" between the Pacific and Indian oceans.
The country's most active volcano, Mount Merapi in central Java, killed more than 350 people in a series of violent eruptions in 2010.
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