While the airport remains in operation, several major carriers have cancelled flights.
Mount Agung last erupted in 1963, killing over 1,600 people, and has been threatening another major eruption since August.
"At 6.20am (local time), the eruption reached between 3,000 and 4,000m from the summit with the ash moving in a southeast direction at a speed of 18km an hour", said the National Disaster Mitigation Agency's spokesman Sutopo Purwo Nugroho in a statement on Sunday morning.
Satellite imagery Sunday showed the volcanic ash drifting east and southeastward towards Lombok Island.
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.
There have been no new evacuations in Bali and a six kilometre exclusion zone around the volcano has not been extended. Government officials are insistent that the island remains safe for now outside of the area immediately surrounding Mount Agung.
Bali is a popular tourist destination for many in the region, with thousands traveling to the island for end of year celebrations.
There are fears the volcano could erupt for the first time since 1963, when almost 1,600 people died.
Mount Agung's alert status was raised to the highest in September following a dramatic increase in tremors from the volcano, which doubled the exclusion zone around the crater and prompted more than 140,000 people to leave the area.
While many have since returned, more than 25,000 people remain evacuated in over 200 temporary shelters. "Seismic activity is characterized by low frequency earthquakes".
Indonesia sits on the "Pacific Ring of Fire" and has more than 120 active volcanoes.