Shaimaa Mounir, a student activist, said the dead student was Khaled El-Haddad, a supporter of the Brotherhood, which was designated as a terrorist organisation this week by the state.
Security forces fired teargas to disperse pro-Brotherhood students who were preventing classmates from entering university buildings to take exams and protestors threw rocks at police and set tyres alight.
A health ministry official said one student had been killed and five injured.
The violence followed clashes across the country on Friday in which at least five people were killed.
Two college buildings caught fire in the violence, sending smoke billowing from the faculty of commerce building, while state TV reported that "terrorist students" had also set the agriculture faculty building on fire.
Police arrested 101 students for possession of makeshift weapons, including petrol bombs. Calm had been restored, and scheduled exams had begun after the morning clashes.
Al-Azhar, a respected centre of Sunni Islamic learning, has for months been the scene of protests against what the Brotherhood calls a "military coup" that deposed Islamist Mohamed Mursi as president.
Meanwhile, a prosecutor ordered the detention to continue of seven Al-Azhar students arrested during clashes on Thursday.
Judicial sources said the students are being investigated on accusations of membership of a terrorist organisation.
The students are the first to be ordered detained by the prosecutor on accusations of belonging to a terrorist group since the Brotherhood was declared as such on December 25.
The move increased penalties for dissent against the government installed after the army ousted Mursi in July following mass protests against his rule.
The widening crackdown against the movement, which was elected to power after veteran leader Hosni Mubarak was toppled in 2011, has increased tension in a country suffering the worst internal strife of its modern history.
The army-backed administration appears determined to clamp down on dissent ahead of a referendum on a new constitution next month, in a step that will pave the way for parliamentary and presidential elections.
Thousands of Brotherhood members have been arrested, with more than 250 supporters arrested on Friday alone.
Analysts say the government decision points to the influence wielded by hawks in the security services. Some officials, including Interior Minister Mohamed Ibrahim, were appointed by Mursi but sided with the army and have been key players in the crackdown.
Human Rights Watch said designating the Brotherhood as terrorist was "politically driven" and aimed at halting the group's activities.
"By rushing to point the finger at the Brotherhood without investigations or evidence, the government seems motivated solely by its desire to crush a major opposition movement," said Sarah Leah Whitson of the New York-based rights group.