The bomb planted on the side of a road exploded as a police convoy was passing through the Ain Shams district in east Cairo, the ministry said in a statement.
It wounded two passersby. One of them later died in hospital, it said.
The attack came days after a suspected Islamist group shot dead a senior army officer in a Cairo suburb.
Islamist militants have waged an insurgency that has killed hundreds of policemen and soldiers since the military ouster of Islamist president Mohamed Morsi in 2013.
Most of the militant attacks are conducted by the Islamic State group's Egypt branch in the Sinai Peninsula although they have spread elsewhere in the country.
A group that calls itself Liwaa al-Thawra -- The Revolution Brigade -- claimed responsibility for assassinating the army brigadier general on October 22.
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