Sheikh Mohamed Tantawi, dean of al-Azhar university, said full-face veiling (niqab) is merely a tradition that has nothing to do with the Islamic faith.
Although most Muslim women in Egypt wear the Islamic headscarf, increasing numbers are adopting the niqab as well.
The niqab question reportedly arose when Sheikh Tantawi was visiting a girls’ school in Cairo at the weekend and asked one of the students to remove her niqab.
Egypt's parliament has rejected a request from two opposition lawmakers to seek the dismissal of the country's top Islamic cleric over his planned ban on women's veils at a top university, Al Jazeera reported.
Muhammad Sayed Tantawi is planning to bar female students wearing Islamic niqab from the schools of Al Azhar University, saying the garment has "nothing to do with Islam."
A Muslim Brotherhood spokesman told the Qatar-based news network that preventing women from wearing veils would "undermine our moral foundations and mutual respect," and "discredit Islam."
Group members Hamdi Hassan and Ibrahim Abu Auf have urged parliament to formally ask Prime Minister Ahmed Nazif to dismiss the cleric over the "illegal" ban.
However, their request was rejected by the 454-seat lower house. The Muslim Brotherhood has just 88 seats in the chamber.
The proposed ban has been widely seen as part of the Egyptian leadership's crackdown on resurgent ultra-conservative elements in the country.
On Saturday, dozens of female students protested against the ban outside the university.
Shaikh Ali Abu al-Hasan, the former head of the Fatwa Council at the Islamic Studies Institute (ISI) in Cairo, was quoted by Al Jazeera as saying although women are not required by Islam to cover their faces, Al Azhar University must give them freedom of choice.
"The niqab is not in contravention of the sharia or Egyptian law," he said.