Governor Made Pastika said the evacuation period for people living within 10km of the crater could easily last as long as a month.
Indonesia's disaster management agency said the evacuation had so far been orderly and without panic.
Mount Agung has been hurling clouds of white and dark grey ash about 3000m into the atmosphere since the weekend and lava is welling up in the crater, sometimes reflected as a reddish-yellow glow in the ash plumes.
Its explosions can be heard about 12km away.
