Thirty fire tenders pressed into service have brought the blaze partially under control after hours of fire fight, a government official said.
The fire was first noticed at 2.30 a.m. Thursday, it spread rapidly to engulf large part of the market, which was set up in 1945 in a congested part of north Kolkata.
Disaster management group and Rapid Action Force personnel are at the spot.
"So far there are no reports of any casualty," Fire services and Disaster management Minister Javed Khan said.
"This market is a bit unplanned like any other old market of Kolkata. It seems the electrical wiring and other such things have not been taken care of properly over the years," City Mayor Sovan Chattopadhaya said.