The fire broke out on the first floor of the market around 5:15pm, said Polash Chandra Modok, duty officer at the Fire Service headquarters.
Twenty-five firefighting units rushed in and brought the fire under control around 6:30pm, said Debasish Bardhan, Deputy Director at Fire Service and Civil Defence.
The fire originated from a shop on the northeast side on the first floor of the market, he said, adding that they were yet to know the reason behind the blaze.
However, no casualty was reported in the incident.
Director General of the Fire Service and Civil Defence Brig Gen Sajjad Hossain told reporters at the spot around 8:10pm that 14-15 shops were gutted and 2-3 others partially damaged by the fire.
He said the fire has already been doused and firefighters were working to clean the debris.
Replying to a query, Sajjad said the reason behind the fire could not be ascertained yet.
An investigation committee will be formed that will ascertain the reason behind the fire as well as the extent of loss, he said.
The market has a total of 1,700 shops, including 105 on the first floor.
Narayan Chandra, who owns a shop on the ground floor, said he went to the washroom on the first floor when he saw fire erupting from a mattress shop.
Bablu, owner of a shop on the first floor, said welding work was underway by the mattress shop which caused the fire.
A total of 70-80 shops, including three owned by him, were gutted by the fire, he claimed.