The explosion ripped through the Cairo Security Directorate, severely damaging the building and the adjoining Islamic Museum in Bab El-Khalk district in central Cairo.
The blast, which could be heard six kilometers away, sent smoke rising above the capital as a large number of ambulances rushed to the scene. TV footage showed dense smoke billowing from the building after the blast.
A Health ministry spokesman said that three people were killed and 40 wounded.
Interior ministry spokesman Hani Abdel Latif told state TV that initial investigations showed that a car bomb might have been used in the attack, Al-Ahram online reported.
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The blast comes on the eve of the third anniversary of the 2011 uprising that toppled longtime president Hosni Mubarak.
Egyptian forces have stepped up crackdown on Islamists whose attacks on the army and police rose dramatically following the ouster of president Mohamed Morsi last July.
The authorities have carried out a sustained crackdown on Morsi's Muslim Brotherhood, which was recently designated a terrorist organisation.
Brotherhood and its partners are planning protests after Friday prayers today across the country, the latest in a series of demonstrations against the overthrow of Morsi.