Five bodies, including one of a four year-old girl, have so far been pulled from the debris of the 36-apartment building. One woman is in hospital in intensive care.
Although the accident took place in the morning, when the majority of the building's residents had already left for work, rescuers said that the death toll was likely to rise significantly. The city hospitals have been put on standby.
The mayor said that the building's owner had carried out illegal reconstruction, ignoring repeated orders to cease.
"Some workers had been working on the first floor, when suddenly the building tilted to one side and collapsed," Adel Labib said.
Rescuers also evacuated residents of two nearby buildings severely damaged in the collapse.
Safety violations have repeatedly caused building collapses all over Egypt. In November 2006, seven people died under the rubble of a collapsed four-storey building in the city of Mansura in northern Egypt. A year before, the illegal addition of three storeys to a residential building in Alexandria resulted in 19 deaths.