Karnataka Home Minister V S Acharya said five persons are feared dead.
Some casualties apparently occured when a few people jumped out of the building in panic, eyewitnesses said.
TV visuals showed one girl clad in a blue slawar kameez landing on the roof of the portico after jumping from the sixth floor and then falling over to the ground. Her condition was not immediately known.
The multi-storey building located on the busy Old Airport Road in Domlur area was completely evacuated and the fire brought under control nearly two hours after it broke out, officials said.
Scores of persons fainted after inhaling the smoke and had to be rushed to nearby hospital for first aid, a senior fire official said.