Residents were evacuated and disaster management team reached the spot.
30 fire engines were at the spot, fire under control but not completely doused.
The building nearly gutted creating panic among the residents.
The fire intensified due to the presence of inflammable material, including plastic and gas cylinders in the godown, a senior official of the fire department said.
"There is no report of any casualty so far and a few persons who were trapped inside the building have been rescued," the official said, adding people living in the adjacent buildings were also evacuated fearing the building might collapse.
"It is a massive fire and we are trying to douse it, but the thick smoke is making it difficult for us to reach the spot since the building is located in a congested area behind Burrabazar police station. The blaze is also spreading fast due to the presence of inflammable materials," he said.
Later, a disaster management team also joined the fire fighting operation, a police source said.
State Fire Service Minister Sovan Chatterjee, who rushed to the spot, said, "We are trying hard to douse the fire and several steps have been taken to prevent the fire from spreading in the adjoining areas. Our senior officers are here."
"Water tank of Nakhoda mosque is being used by the fire fighters as the water source," he added.
Chatterjee, who is also the mayor of the city, supervised the fire-fighting operations. Two to three LPG cylinders were taken out during the evacuation in his presence, a fire department personnel said.
"The entire area has been cordoned off. Traffic at Rabindra Sarani has been stopped while the traffic on M G Road was restricted," a police officer said.