The unrest followed nationwide repression of Islamist protests on Friday after the military-installed government listed the Brotherhood, the movement of deposed president Muhammad Mursi, as a terrorist organization.
A hospital official said a 19-year-old student was shot dead in the clashes at the Al-Azhar University campus, where pro-Mursi students have regularly staged protests since his overthrow by the army in July.
The students 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.
Police also fired tear gas at students in Zagazig university north of Cairo on Saturday, security officials said.
And elsewhere in Cairo, police said they defused a bomb found on a bus days after four people were wounded when an explosive went off next to another bus.
The military-installed government has banned protests by Brotherhood members demanding Mursi’s reinstatement, after listing the movement as a terrorist organization 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 Mursi on July 3, despite a crackdown that has killed more than 1,000 people, mainly Islamists, and imprisoned thousands.
It was listed as a terrorist group in a drastic escalation of the months-long crackdown after a suicide bombing killed 15 people in police headquarters north of Cairo on Tuesday.
The attack was claimed by an Al-Qaeda-inspired group that has led attacks on the military and police and in the restive Sinai peninsula, and denounced by the Brotherhood.
Five people were also wounded in a bomb that targeted a bus in Cairo on Thursday.
On Friday, the Brotherhood, which had dominated elections following the overthrow of strongman Hosni Mubarak in early 2011, said it would remain committed to peaceful protests.
“The Muslim Brotherhood declares it is innocent of any violent incident that has or will be committed,” the Islamists said in a statement.
The interim government has decapitated the 85-year-old movement since Mursi’s overthrow, imprisoning him and most of the movement’s leadership and putting them on trial.
It has also sought to quell a surge in attacks in the Sinai that has killed more than 100 soldiers and policemen, as bombings and shootings spill over into mainland Egypt.
Ansar Beit Al-Maqdis, the group that claimed responsibility for Tuesday’s police headquarters attack, had tried to assassinate the interior minister Mohamed Ibrahim in a suicide car bombing outside his home in Cairo in September.
The militant group has criticized the Brotherhood for its style of electoral politics, but authorities say the movement has links with militant groups, without offering proof.
Mursi himself and top Brotherhood leaders will face trial with top Brotherhood leaders for allegedly colluding with militants to carry out attacks.
Mursi, Egypt’s democratically elected president, had ruled for one turbulent year before the military overthrew him, following mass protests demanding his resignation