Gunung Agung last erupted in 1963-1964, killing approximately 1,500 people.
Around 62,000 people lived in the danger zone before the evacuations, according to the agency, but residents just outside the area have also left as a precaution.
President Joko Widodo was expected to visit evacuation centres on Bali later on Tuesday. Mount Agung, 75 kilometres (47 miles) from the tourist hub of Kuta, has been shaking since August and threatening to erupt for the first time in more than 50 years. More than 500,000 people evacuated when Mount Merapi in central Java erupted in 2010, more than double the population in the exclusion zone around that volcano, he said.
"There will definitely be an impact on (sales of) tour packages but we don't know the figures yet", said Agustinus Pake Seko of PT Bayu Buana travel agency.
"Mount Agung is one of many similar volcanoes in Indonesia and the ring of fire surrounding the Pacific and eastern Indian oceans", he wrote. However, embassies have warned of possible flight cancellations in the event of an eruption.More news: Foldable Samsung Galaxy X could launch in January 2018
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Karangasem regency, where Mount Agung is located, is housing the largest number of evacuees, with 21,280 people spread across 84 shelters.
So far flights to the holiday island have been running to schedule.
"Business is getting low since Mount Agung's alert status was raised to the highest level", said Ketut Purnawata, manager of Dasawana Resort, which is in the same district as the volcano, normally popular with tourists and hikers.
At 11am BST EMSC, an independent scientific organisation that provides real-time natural disaster warnings, tweeted: "Strongest quake so far while the volcano may be about to erupt".
The reminder follows a warning issued by local authorities following the possibility of a volcanic eruption.
A spokesman from the Association of British Travel Agents (ABTA) said: "The Indonesian authorities have kept the alert level at the highest classification, meaning an eruption could be imminent".