The Indonesian authorities have declared a radius of nine kilometres around the mountain dangerous. They said the danger level is entering a "critical phase" and have raised the alert level to IV.
The people who have left the area are said to be around 122,500. The volcano is located around 70 kilometers (43 miles) north of Bali's main tourist areas of Kuta and Seminyak, CNN quoted the Indonesian National Disaster Management Agency, as saying.
The official exclusion zone extends 12 kilometers from Mount Agung. The volcano erupted last in 1963.
Meanwhile, the Ministry of External Affairs in India has issued a travel advisory for Indian nationals travelling to Bali to "keep abreast with the latest situation through their respective airline and tour operators before finalizing travel plans.
It said that non-essential travel should be deferred till the alert level is lowered.
"For those already in Bali, it would be safer to avoid travelling to north and east Bali. Please keep in touch with your hotel and tour operators," the MEA statement said.
"In case of emergency and distress, please contact the Consulate General of India, Bali at +628113976388 or +628113867270 or tweet @cgibali", the statement added.
Bali's Ngurah Rai airport (Denpasar International Airport) has been prepared for an emergency operations centre, in the event of an eruption closing the busy airport.(ANI)