Two civilians succumbed to their injuries hours after the blast, according to a health ministry official.
The area surrounding the building - which houses the General Prosecutor's office and is the headquarters of some of the country's most senior courts - was searched by explosives experts who found no more explosive devices.
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.
It was the second time a bomb went off near the supreme court, after an explosion wounded 12 people in October last year.
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Today's explosion came days after a series of bombings in Cairo in which one person was killed.
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.