Sunan Kalijaga State Islamic University said it issued the edict this week to more than three dozen niqab-wearing students, who will be booted from school if they refuse.
Although niqabs are common in ultra-conservative Saudi Arabia and some other Gulf states, they're rare in secular Indonesia, where around 90 percent of its 260 million people have traditionally followed a moderate form of Islam.
For many Indonesians, the niqab -- a full veil with a small slit for the eyes -- is an unwelcome Arab export and some associate it with radical Islam, which the country has wrestled with for years.
The school, based in Indonesia's cultural capital Yogyakarta, has some 10,000 students.
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Another Yogyakarta-based institution, Ahmad Dahlan University, has also introduced a new prohibition on the niqab out of fears it might stir up religious radicalism, which has seen a resurgence on many of the nation's university campuses.
There will be no penalty for those who refuse, it added.
"But during exams, they cannot wear it because officials have to match the photos on their exam ID with them, which is hard if one is wearing the niqab," university chancellor Kasiyarno, who like many Indonesians goes by one name, told reporters yesterday.
The niqab has been at the centre of a heated global debate over religious freedom and women's rights, with France the first European country to ban it in public spaces.
Backers of the schools' new rules said wearing a niqab is not a religious obligation.
"Education should be about dialogue -- open and progressive -- and if you wear a niqab it interferes in that dialogue and the teaching-learning process," said Zuhairi Misrawi, head of the Jakarta-based Muslim Moderate Society.
It's "a matter of personal preference and the university has to respect that", said Fadlun Amin, a spokesman for the local chapter of the Forum Ukhuwah Islamiyah, part of top clerical body the Indonesian Ulema Council.
Several Indonesian universities have issued niqab bans in the past.
Last year, a private Islamic high school in Java was reprimanded by local officials after images went viral online that showed a classroom of sitting female students wearing niqab, violating a national regulation on acceptable school uniforms.