Officials issued a red alert after Mount Sinabung began to spew lava shortly after midnight (1900 GMT).
Smoke and ash reportedly shot 1,500m into the air, and witnesses said they could see lava from the volcano from several miles away.
Mount Sinabung, some 60km (40 miles) south-west of Sumatra's main city Medan, has not erupted for 400 years.
The volcano had been pumping out smoke all day Saturday, but alert levels had not been raised, and local media reported that villagers had been taken by surprise.
The Medan Tribune quoted one local resident as saying he panicked and ran when he saw lava coming towards his him "like a ball of fire".
Priyadi Kardono from Indonesia's National Disaster Management Agency told the BBC that more than 10,000 people were being evacuated from nearby villages.
But he added that some had already gone home as volcanic activity was decreasing.
Surono, head of the nation's volcano disaster alert centre, told AFP news agency that the alert level had been raised to red because the situation was "clearly dangerous".
"Initially we thought the ash and smoke were triggered by rain but now we know the driving pressure was from magma," he said.
The Indonesian archipelago lies on the Pacific "Ring of Fire" and has at least 129 active volcanoes.