The protesters claim the Muslim Brotherhood wants to push Al-Azhar Grand Imam Ahmed el-Tayeb out so it can control the school, a leading center of Islamic learning, Ahram Online reported.
Al-Masry al-Youm reported the crowds in Luxor swelled near 10,000 people after Friday prayers and hundreds of others rallied in Cairo as well.
Protesters hoisted signs warning "Al-Azhar is a red line" and chanted against the Muslim Brotherhood, shouting "Blood and soul, we sacrifice for you, Tayeb," and "Oh Imam, we are with you against the Brothers," al-Masry al-Youm reported.
Calls for the grand imam's removal came after an outbreak of food poisoning at the university Monday sickened more than 500 students. The university's president has been fired and the head of the dormitory where the food poisoning occurred was taken into custody.
The Press Trust of India reported Egypt's Grand Mufti Shawky Ibrahim Abdel-Karim Allam warned Thursday against those who would try to pull Al-Azhar University into the country's political fray
"We call on all Egyptians to refrain from dragging Al-Azhar into political matters and grievances because this is the only way in which the moderate version of Islam and our institution's independence will persist," Allam said.
He said such behavior, including attempts to oust el-Tayeb, "undermines Egypt's security."
After the food sickness outbreak, officials summoned the head of the university's dorms, Mohamed Reda, as well as Al-Azhar University President Osama al-Abd, for questioning, al-Masry al-Youm said.
Prosecutors also were investigating three other university officials in the incident.
The university's top leadership caved to students demands and dismissed Abd Wednesday. The Al-Azhar Supreme Council has called for immediate elections to choose a new president, al-Masry al-Youm reported.
The council has already appointed a new director general of the dormitories, as a well as a new food and beverage manager and a new head of the dorms.