The confrontations came as pro-Morsi groups called for a week of anti-military protests under the slogan "Massacre of the Century".
That is a reference to the August 14 crackdown by security forces on Morsi supporters in Cairo's Rabaa al-Adawiya Square where at least 627 people died on that day.
The boy, aged 10, was hit in the head by a bullet when pro-Morsi marchers clashed with his opponents after Friday prayers in the city of Suez, security officials said.
Khaled al-Khatib, a senior health ministry official, confirmed the two deaths to state news agency MENA, adding that another 15 people were injured nationwide.
Disturbances were also reported in some districts of the capital and in other towns.
Police fired tear gas as pro- and anti-Morsi students pelted each other with rocks at Cairo's Al-Azhar University, security officials said.
An interior ministry statement said that some students linked to the Muslim Brotherhood torched a tram carriage in the Heliopolis district of the city.
Last day, Egypt's interim rulers gave police the power to enter university campuses to quell protests without seeking prior permission from the prosecutor general or university authorities as previously required.
Fighting also erupted in the oasis city of Fayoum some 100 kilometres (60 miles) south of Cairo, and was later broken up by police using tear gas.
At least 27 people were arrested nationwide, MENA reported.
Islamist supporters of Morsi have regularly staged demonstrations against the military-installed authorities since his ouster by the army on July 3.
The interim authorities are engaged in a sweeping crackdown targeting Islamists, and more than 1,000 people have died in violence since then.
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