The undersea natural disaster struck 125km (77 miles) northeast of Surabaya on Thursday, followed by at least 400 tremors.
They are living in temporary shelters, sports centers, village halls and with relatives, said agency spokesman Sutopo Purwo Nugroho.
However, flights at Bali’s global airport were operating as normal and there was little disruption to tourism operators across the rest of the island, authorities said.
Others packed their belongings into trucks for evacuation, while more stopped to watch as clouds of white smoke rose from the crater, which is around 3,000 meters (9,840 feet) above sea level.
The agency said there had been increased seismic activity as well as 50-metre-high blasts from the volcano’s centre.
Indonesia is located in the so-called ‘Pacific Ring of Fire, ‘ the meeting place of several tectonic plates which leads to roughly 90 percent of the world’s seismic activity.
Indonesia, an archipelagic nation with over 17,500 islands, has a total of 129 active volcanoes.
The Mount Agung volcano, or Gunung Agung, about 70 kilometres from Kuta on the holiday island last erupted in 1963 killing more than 1,100 people.