The area surrounding the building houses the General Prosecutor's office and is the headquarters of some of the country's most senior courts.
The bomb was hidden under a car parked near the Supreme Court, the country's highest criminal court, and went off in Cairo's downtown area.
The area is very crowded, with dozens of street vendors selling their ware on stalls set up on the asphalt. Nearby are several bus stops, a railway station and a subway station.
Abdel Ghafar said that one of the injured is in a critical condition. The injured include five policemen.
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Earlier reports issued by state TV said that a person was killed during the explosion, however, the ministry of health confirmed no deaths.
Egypt has witnessed many attacks targeting police and military personnel as well as civilians in the recent period.
The attacks have increased after the ouster of Islamist ex-president Mohamed Morsi in 2013. Over 500 policemen and soldiers, have been killed in the attacks.