The explosion took place outside a fruit stall stationed on the ground floor in the market at 9:30 in the morning in the congested Kazipara area.
The injured have been rushed to the state-run R G Kar Medical College and Hospital, police officer said.
The area of incident falls under the jurisdiction of Barrackpore Police Commissionerate, and police have rushed to the spot.
The police officer added, the building in which the explosion took place also houses the office of South Dum Dum Municipality Chairman.
Fire tenders have also been deputed in the affected area and a forensic team and sniffer dogs have been arrived to the spot to ascertain the nature of explosion, police said.
The cause of the explosion is yet to be ascertained.