The fire broke out around 5:30 am on Thursday, said Mahfuz Riben, an official of the fire service's control room.
Twelve units of the fire service tamed the flames after an hour's efforts.
The cause of the fire or the extent of the damages could not be determined immediately.
The kitchen market which stands beside Malibagh Super Market houses a total 50 stores. It is surrounded by numerous residential buildings and hotels.
Meanwhile, a fire erupted in a television warehouse on the basement of a madrasa in Jatrabari's Kutubkhali in the early hours of Thursday.
Nine units of the fire service successfully doused the flames around 3:45 am, said Farhad Alam, an official of the fire service's control room.
The fire service could not immediately identify the cause of the fire or extent of the damages inflicted by the flames.