Five fire-tenders fought the fire at a branch of the Syndicate Bank housed in a multi-storey building, the police said. The fire started at around 9.40 am.
The residential building was partially evacuated and a unit of the disaster management team of the Kolkata police went to the spot.
The fire is yet to be fully controlled, a senior police official said.
"The cause of the fire is not yet known. It seems that the blaze started at the central air conditioning system," he said.