The fire started on the second floor of the building on road No. 113 around 11 am Wednesday, according to Saifuzzaman, deputy assistant director of the Fire Service.
Three units of the Fire Service subsequently tamed the flames after an hour, he said.
"Seven people have been taken to the hospital. Our work is ongoing and we are trying to determine the cause of the fire."
The building has a parking facility on the ground floor while there is a total of 10 apartment units on the floors above.
The fire was sparked by an AC explosion on a second-floor flat, according to the building's security guard.
Almost all the rooms in the flat were burnt down before the fire spread to the third and fourth floors.
A woman living on the sixth floor said panic spread throughout the building after the fire broke out as residents rushed out of their homes with their children.