The student was hit in the head by birdshot during the clashes and five other students were arrested, al-Ahram reported, adding that students threw rocks and bricks at security forces from behind the campus walls late on Wednesday.
Security forces stormed into the university, state news agency MENA reported, after they were called in to control the protesters who set fire to trees inside the campus.
Supporters of Morsi's Muslim Brotherhood protest frequently at the university, which is in the same Cairo suburb as the Rabaa al-Adawiya mosque, scene of a pro-Morsi protest camp where thousands were killed when it was stormed by security forces on Aug. 14.
The students organized the al-Azhar University protest to demand the release of jailed student activists who were arrested after previous clashes at the university.
Egypt plunged into violence after July 3, when the army removed Morsi from office, suspended the constitution, and dissolved the parliament. It also appointed the head of the Supreme Constitutional Court, Adly Mahmoud Mansour, as interim president.
NTJ/NJF