The National Disaster Mitigation Agency said the ash column from Mount Agung rose 1500m following an eruption at about 5:30pm on Saturday.
Disaster agency spokesman Sutopo Purwo Nugroho said in total, eight worldwide flights to Bali and 13 global flights departing from Bali were cancelled.
Qantas, Virgin and Dutch airline KLM soon followed Jetstar's lead in cancelling flights.
"As a result we have cancelled flights to and from Bali this evening".
Hengki Heriandono, acting corporate secretary of national flag carrier Garuda Indonesia, earlier said the airline cancelled all of its 18 flights to and from Lombok.
Authorities have told people within a 7.5km exclusion zone to "immediately evacuate" in an "orderly and calm manner".
Magma - molten rock - has now been detected close to the volcano's surface, said officials and volcanologists.
JOHANNES CHRISTO REUTERS There is an exclusion zone around the volcano
The airport authority is preparing for the worst-case scenario - a total closure caused by a shifting ash cloud, Herson said. Suantika said Agung could spew ash for at least a month but did not expect a major eruption.
Bali is a popular tourist destination for many in the region, with thousands traveling to the island for end of year celebrations.
About 25,000 people have been unable to return to their homes since September, when Agung showed signs of activity for the first time in more than half a century.
When the volcano last erupted in 1963, it killed more than 1,000 people and destroyed several villages, remaining one of the largest and most devastating eruptions in the Southeast Asian country's history.
The Mt. Agung volcano, which towers over eastern Bali at a height of just over 3,000 meters (9,800 feet), is about 70 kilometers (43 miles) from the island's main tourist areas of Kuta and Seminyak.
It is home to more than 130 active volcanoes. "Seismic activity is characterized by low frequency earthquakes".