"Armed men on a motorcycle opened fire on the police before fleeing," ministry spokesman Hani Abdel Latif told AFP.
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The police officers had been guarding branches of two foreign banks, Britain's HSBC and Union National Bank of the United Arab Emirates, when they were attacked near a Cairo square.
Scores of policemen and soldiers have been killed in bombings and shootings since the Egyptian military deposed Islamist president Mohamed Morsi in July 2013.
Most of the attacks have been in the Sinai Peninsula, the deadliest of them claimed by Beit al-Maqdis, a militant group that has pledged allegiance to the Islamic State organisation.