Aljazeera's correspondent in Egypt reported that 16 people are still thought to be trapped under the rubble.
The body of a young boy and a middle-aged man had been pulled from the ruined building, witnesses said.
Rescue workers were still digging through the remains of the building.
Television pictures showed a large pile of collapsed masonry in a residential area.
One police source said the building was originally three storeys high but he said extra levels had been illegally added.
No reason as to what caused the buidling to collapse was given.
The collapse of apartment blocks is not uncommon in Egypt, where regulations are sometimes ignored and residents often add unauthorised floors to existing structures.
Five people from one family were killed in another building collapse in Alexandria in June last year.
In the same month, a five-storey building fell in a residential area of the southern city of Aswan, killing 14 people.