The pro-Morsi demonstrations came just a day after the government lifted a state of emergency yesterday and curfew that had been imposed in August after a deadly crackdown on Islamists in Cairo.
The interior ministry said the 16-year-old boy was hit by birdshot during clashes with supporters and opponents of the Islamist leader in the centre of Alexandria and died on his way to hospital.
Without elaborating, it said in a statement that demonstrators from the banned Muslim Brotherhood had fired on their opponents during the clashes in the Mediterranean city.
The marchers chanted slogans hostile to General Abdel Fattah al-Sissi, the military chief who overthrew Morsi in July after millions of Egyptians took to the streets demanding the Islamist president's resignation.
Also Read
After Egypt's first democratically elected president was deposed his Muslim Brotherhood movement staged rallies and set up protest camps in Cairo to demand his reinstatement.
The security forces dispersed them in August in a bloody crackdown that left hundreds dead, and more than 2,000 Islamists have been arrested since then.
State news agency MENA reported that thousands of pro-Morsi supporters also demonstrated in the city of Fayyum, south of Cairo.
Morsi, who was arrested after his July 3 ouster, has been charged with inciting the murder of protesters outside the presidential palace in December 2012.
His trial, along with 14 other defendants, opened on November 4 and is set to resume in January.