Seventy people have been injured, a spokesman for the local fire brigade has told the BBC.
Firefighters have now entered the building after the fire was brought under control.
The death toll may rise further, as dozens are feared trapped inside the 19-storey office block in Banani.
They are believed to have been situated on the upper floors of the building, above where the fire broke out.
Local media said people were seen shouting for help from windows and at least six people jumped out of the burning building.
