Fires were set in the business and agriculture faculty buildings at Al Azhar University as students clashed with police, the BBC reported.
At least one person was killed, Ahram Online reported.
Several students demanding the reinstatement of former president Mohamed Morsi were injured when security forces shot at them, the university's student union said in a post on its Facebook page. An engineering student was reportedly in critical condition after being shot in the head.
A faculty dean, Bakr Zaki, said students and others not associated with the university had locked the gates in the morning in an attempt to stop faculty and students from entering.
Several students were injured as they tried to enter the campus to take final exams.
The Muslim Brotherhood, of which Morsi is a member, was declared a terrorist organization Wednesday by Egypt's interim government.