The tragedy occurred early Wednesday when most of the apartment building's 35 residents were at home.
Rescuers are continuing to search the rubble for survivors and the authorities have opened an investigation into the incident.
Such accidents are common in Egypt, which has around 2 million buildings in a dangerous condition. State agencies have issued over 100,000 notices condemning unsafe and improperly built structures, but the majority of them have been ignored by residents and owners.
Safety violations have been the cause of numerous building collapses in the country. In September, more than 100 people died when falling rocks flattened a densely populated Cairo shanty town. In December 2007, a 12-story building in Alexandria collapsed, burying around 30 people under the debris.
