Armed Forces and Civil Defense personnel were trying to locate survivors but said the number of victims likely would increase, al-Masry al-Youm reported.
At least 10 people were injured, rescue personnel said.
Nasser al-Abd, head of the city's investigation office, told the newspaper the building has 24 apartments and was built five years ago.
The official said sewage runoff created a crack in the building's foundation about two years ago.
Al-Masry al-Youm reported the owners were arrested and would be charged with homicide, deliberately causing injury and building without a license.