In a statement, the university claimed that it had been proven that the dismissed students were involved in violence on campus since the new academic year began in early October.
University administrators urged other students to abide by university regulations, adding that upcoming exams would be held according to schedule on January 4.
Students expelled from one university in Egypt cannot enroll in another, in line with amendments introduced to university bylaws last year by then-Interim President Adly Mansour.
In late October, President Abdel-Fattah al-Sisi approved new legislation giving university presidents the right to dismiss students involved in campus protests or riots.
Al-Azhar University has become a center of protests in support of former President Mohamed Morsi, who was ousted by the military in July of last year.
Egyptian security agencies accuse Morsi's Muslim Brotherhood group of using university students as tools to oppose the current authorities.
The Brotherhood calls Morsi's ouster last year a "military coup." Others, however, call his ouster a "popular uprising," as Morsi was unseated by the army following massive opposition protests.