Thousands of the Islamist's backers had rallied across the country before police intervened to disperse the protests with tear gas and birdshot.
The protests came after an Islamist alliance backing Morsi called for demonstrations ahead of a new hearing in Morsi's trial on Wednesday.
One man was killed by birdshot to his chest in the Suez canal city of Ismailiya during clashes after weekly Muslim prayers, medics said, adding that eight others, including a police officer, were wounded.
And in the Mediterranean city of Alexandria, a third person was killed, officials said.
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At least 122 people have also been arrested around the country, they said.
Police also fought street battles with rock-throwing protesters in several districts of the capital.
Protesters in Cairo torched a police vehicle using petrol bombs, a security official said. State media said residents extinguished the fire.
In the upscale Maadi neighbourhood, police fired tear gas near a military hospital as protesters threw fireworks at them, an AFP reporter said.
The street was littered with rocks and burning wood as police vehicles sped up and down the road to disperse the protesters.
The demonstrators regrouped in a side street, facing off with riot police and chanting "They are the thugs!"
Some protesters threw stones.
In an eastern neighbourhood of Cairo, police also used tear gas against thousands of Morsi supporters who burnt tyres and threw fireworks at security forces, another AFP correspondent said.
Gunshots were also heard.
Protesters chanted "Down with military rule" and slogans against army chief Abdel Fattah al-Sissi, who led Morsi's ouster in July.
They included Tahrir Square, as well as Rabaa al-Adawiya and Nahda squares, which were the sites of a bloody crackdown on Morsi's supporters in August.
State news agency MENA reported a number were wounded by birdshot in clashes in Alexandria and that Morsi supporters torched two civilian cars.
Since the Islamist president's ouster, his supporters have staged near-daily protests calling for his reinstatement, particularly after Friday prayers.
But their numbers have dwindled amid a violent government crackdown.