The building is located near Afghan Church in Colaba, South Mumbai. The fire is reported to started in the third floor of Assaye Building.
According to fire department officials, they were notified of the fire at 7.22 pm.
Four fire engines and an equal number of water tankers have reached the site and are trying to control the fire.
Brihanmumbai Municipal Corporation officials told news agency Press Trust of India that the required agencies had been mobilised. There are no reports of casualties so far.
The fire at Army office building in Colaba has been brought under control. No injuries have been reported. Damage due to the fire is being assessed in two office rooms, a Defence Ministry spokesperson told news agency ANI.