A police official said a street vendor was shot dead in clashes between Morsi's Islamist supporters and civilian opponents in the Mediterranean city of Alexandria.
The Islamists had held rallies in several cities demanding the reinstatement of Morsi, who the military ousted in July following mass protests demanding his resignation.
The interior ministry said police arrested 47 suspected protesters in several cities.
State television reported one police officer was wounded in the clashes.
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The Islamists have organised near daily protests since Morsi's overthrow, often clashing with police and civilian opponents.
At least 17 people were killed across the country on January 3 and more than 100 were arrested, as police clamped down on Morsi's Muslim Brotherhood movement that has spearheaded the protests.
The government last month designated the Brotherhood movement as a terrorist organisation, outlawing membership or support for the Islamists.