The policeman was hit by a bullet in the chest as he took an arrested protester to a police van after security forces broke up the protest on the outskirts of the capital's upscale Maadi district, the ministry said on its Facebook page.
He was declared dead on arrival at hospital, it said, adding that the bullet that killed him was fired from a nearby building.
The pro-Morsi demonstration came after the Islamist Anti-Coup Alliance called for a week of protests from today under the slogan "Freedom For Egypt".
State television also reported the policeman's killing, and in a separate report the official MENA news agency said at least 65 protesters were arrested nationwide today.
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Morsi was ousted by former army chief Abdel Fattah al-Sisi, who last month overwhelmingly won a presidential election that was boycotted by the Muslim Brotherhood, the Islamist movement to which Morsi belongs.
Since Morsi's removal, a government crackdown on the Muslim Brotherhood and its supporters has killed more than 1,400 people and jailed upwards of 15,000.
Hundreds have also been sentenced to death in often speedy trials.