A hospital official said a 19-year-old student was shot dead in the clashes at the Al-Azhar University campus, where pro-Morsi students have regularly staged protests since his overthrow by the army in July.
The students had entered the commerce faculty during an exam and set it alight, before police burst into the campus and fired tear gas.
A police official said 60 of the students were arrested after the fire on the first two floors of the building was brought under control. The violence comes a day after five people were killed in clashes across Egypt, according to a health ministry tally on Saturday, as police stamped out Brotherhood demonstrations.
The interior ministry said 265 protesters were arrested. The military-installed government has banned protests by Brotherhood members demanding Morsi’s reinstatement, after listing the Islamist movement as a terrorist organisation this week.
The designation carries harsh penalties, with Brotherhood leaders facing possible death sentences and protesters looking at up to five years in prison.
The movement has held near-daily protests since the military ousted Morsi on July 3, despite a crackdown that has killed over 1,000 people, mainly Islamists, and imprisoned thousands.