Mount Sangeang Api began erupting on Friday and plumes of ash have been sweeping south towards Australia.
Qantas, Jetstar and Virgin Australia have all cancelled flights. Services between Australia and the province of Bali have also been hit.
The authorities say other airports could be affected in the coming days.
Hundreds of passengers have been caught up, with disruption expected to continue until at least Sunday.
“The volcano is undergoing a sustained, rather significant eruption at the moment,” Emile Jansons, manager of the Darwin Volcanic Ash Advisory Centre told Reuters news agency.
“For the last 10 hours we’ve been observing large masses of volcanic ash being generated.
“Nobody has a very good handle on what this volcano is likely to do in the next 24 hours or beyond.”
Some flights between Perth and Bali were cancelled on Saturday.
Volcanic ash can be extremely dangerous to aircraft as the fine particles can damage engines.
The cloud is now sweeping south towards as Alice Springs, officials say.
Deputy PM Warren Truss said it could take days for Australian services to return to normal.
“Depending on wind and other weather conditions, the ash has the potential to affect flights to and from other airports, including Brisbane, during coming days,” he said.
The island of Sangeang Api has no permanent residents after they vacated following an eruption in 1988. Farmers nearby have reportedly been told to leave the area.
Indonesia lies across a series of geological fault-lines and is prone to frequent earthquakes and volcanic eruptions.
There are about 130 active volcanoes in Indonesia.
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