All flights were cancelled at 7am local time on Monday and the airport will remain closed until further notice.
There had been fears the situation would worsen overnight and the airport had prepared for the worst.
'Once the airports find volcanic ash trace, we'll close down the airport for flights,' the chief of the airport told the ABC on Sunday.
Authorities raised the volcano alert to the highest level on Monday and ordered people within 10km of the mountain to evacuate amid fears of a major eruption.
Magma has now reached the surface of the volcano, which threatens to produce a 'strong, explosive eruption,' authorities warned.
Over the past months, 140,000 people have been evacuated from the region around the volcano when it was on high alert but that number is reduced to about 30,000 after the alert levels were lowered.
Indonesian authorities downgraded their eruption warning for Mt Agung in late October after a decrease in seismic activity.
The alert was boosted to the highest threat level in September amid fears an explosive eruption was imminent.
Mt Agung’s last major eruption was in 1963 and killed more than 1100 people. That eruption lasted for more than a year.