The cause of the fire could not immediately be determined.
Sen said at least 33 people, including women and children, were declared dead at the Dhaka Medical College Hospital, while at least 10 others died after being taken to the Sheikh Hasina National Institute of Burn and Plastic Surgery.
More than a dozen firefighting units were deployed to douse the fire that broke out at the Green Cozy Cottage Shopping Mall, said Fire Service and Civil Defense Director General Brig. Gen. Md. Main Uddin.
At 75 people, including 42 who were unconscious, were rescued from the building, rescuers said.