Ammar Badie, 38, died of a bullet wound sustained while taking part in protests in Ramses Square, it said on its Facebook page.
The whereabouts of Mohamed Badie, who is the Islamist movement's General Guide, are unknown. He has been charged with inciting violence and faces a trial that starts on August 25. His son's death follows the killing of the daughter of Mohamed El-Beltagi, a senior Brotherhood politician, in protests this week.
Police also detained Brotherhood politician Gamal Heshmat, according to a statement from the Anti Coup Alliance. Heshmat is a leading member of the Freedom and Justice Party.
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