Four people were also arrested during the violence that broke out on the sidelines of a pro-Morsi gathering, the officials said.
Since the Egyptian army ousted and detained Morsi on July 3 last year, the security forces have waged a crackdown on protests by his supporters.
The crackdown has seen more than 1,400 people killed and 15,000 arrested, including nearly the entire leadership of Morsi's Muslim Brotherhood, which the military-installed authorities have banned and declared a "terrorist" group.
The Islamists are expected to step up their protests ahead of a presidential election called for May 26-27.
Former army chief Abdel Fattah al-Sisi, who toppled Morsi, is expected to stroll to victory in the election against his only rival, Hamdeen Sabbahi, a leftist politician.
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