The early morning explosion - one of three to hit the capital yesterday - damaged the Cairo Security Directorate, which includes police and state security, and sent smoke rising over the capital, raising concerns an Islamist insurgency was gathering pace.
Hours after the attack, two more blasts rocked the city.
A crude explosive device killed one policeman and wounded nine others in another Cairo neighbourhood and a third explosion occurred near a police station. The first attack also heavily damaged the nearby Islamic Art Museum.
The office of President Adly Mansour said it would "avenge the deaths of the martyrs" who died at the Security Directorate and severely punish the perpetrators.
There was no immediate claim of responsibility for the attack, which came a day before the third anniversary of the uprising that toppled autocrat Hosni Mubarak and raised hopes of a stable democracy.
Instead, relentless political turmoil and violence have hit investment and tourism hard after the toppling of President Mohamed Mursi, who was elected in 2012.