Five people, including two fire and rescue service personnel, sustained burn injuries and were admitted to hospital.
Police said the process of identifying the dead had begun.
Preliminary reports indicated that the fire broke out in the Axis Bank office in one of the floors of a commercial complex on Avinashi Road, central Coimbatore.
More than 15 fire tenders from Coimbatore and nearby places battled for over two hours to douse the fire.
Helicopters belonging to the armed forces were also pressed into service to rescue people trapped on the roof top of the commercial complex.
Senior district administration and police officials visited the accident spot.
Police said two people who jumped from the building to escape the fire sustained injuries.
Investigators have still to ascertain the cause of the blaze.