Rescue workers pulled out the bodies of four policemen, eight firefighters and two civilians from the buidling which collapsed late on Monday night after a fire broke out.
The collapse also left more than 36 people wounded.
Many of the casualties were firefighters, police or rescue workers who were trying to put out a blaze in the building in a central shopping street when it came crashing down.
Witnesses said the fire appeared to have started in a cellar storing inflammable materials, including aerosols. Police said the blaze also caused several explosions inside the building that housed a popular restaurant.
The subsequent collapse was believed to have been due to shoddy construction.
"I was inside the building, I heard an explosion then I lost consciousness. I found myself in the hospital," said one of the survivors.
Rescue workers said hopes of finding survivors under the debris were slim.
Housing Minister Ibrahim Sulayman said seven floors had been illegally added to the building not five-floors as originally sanctioned.
The collapse left cracks in two adjacent buildings, which had to be evacuated during the night.
Building collapses are not rare in Egypt, where many high-rises are built without authorisation or normal checks.
Seven people died when a building collapsed in Cairo last May.