The group's Facebook account invited fellow students to cover their hair on Wednesday in a bit to to "demystify the veil"
"It's also about showing support to the idea of being in charge of out own bodies. We dress how we want, and don't accept being told otherwise," they wrote.
"Veiled or not, we are all equal."
The group took aim at the "disturbing declarations" of France's women's rights minister, who faced ridicule and calls to resign last month after comparing women who wear the Muslim headscarf and veil to "negroes who supported slavery".
Over 250 people said they would attend the event, which is scheduled to run until 9pm on Wednesday, and pictures on social media suggested that there was a definite interest (see tweets below).
The invitation welcomed men and women to try on the group's "prettiest scarves and pashmina" from 8am, and invited guests to hang around for assistance, tutorials, and discussion.
The university said in a statement sent to The Local that such debates were welcome, as the campus "had always been a place for open debate and free expression".
It added, however, that even though the event was being held on school grounds, the university "can in no way be interpreted as supporting the initiative".
Agnès De Féo, French author and documentary maker who specialises on the subject of the Muslim veil in France, said the "Hijab Day" could have a positive impact.
"It will help de-stigmatize the women who wear the hijab in France and allow women to put themselves in the position of those Muslim women who wear it," she told The Local. "It will encourage people to reflect and ask themselves questions".
De Féo, who is a strong critic of how France has cracked down on both the veil and burqa in recent years, says the widespread notion that women who wear the veil in France only do so because they feel obliged to by their husband is wrong and a "colonialist view".
"I have never met a Muslim woman in France who said she wore the veil because her husband made her."
However, wearing a headscarf for a day is no solution, said Romain Millard, president of the university's Républicains association, was among those against the idea.
"I thought at first that it was a joke," he told Le Figaro newspaper.
He said that while he wasn't against the veil being worn at university, he didn't accept it as "a cultural experience to share".
Others were less forgiving, including Carla Sasiela, the head of the UNI student union.
"This is a provocation and we denounce the religious character of the event," she told The Local.
Her group said the event is a "total contradiction of the values of the Republic and the respect for women's rights".
"The debate isn't about the act of wearing the veil, it's about the promotion of it at Sciences Po," she said.
Veils and headscarves have been a hot debate topic in France in recent years, not least since France banned full-face veils in public back in 2010, in a move referred to as the "burqa-ban".
As recently as this month, Prime Minister Manual Valls said that the headscarf was being used by some as a challenge to France's secular society.
"The veil does not represent a fashion fad, no, it's not a colour one wears, no: it is enslavement of women," he said, warning of the "ideological message that can spread behind religious symbols".
"We have to make a distinction between wearing the veil as a scarf for older women, and it as a political gesture confronting French society."
Valls was criticized for claiming that he believed Islam was compatible with French values before seemingly proving the opposite by calling for a ban on the hijab at universities.
Agnes de Feo called the Prime Minister's stance "pure hypocrisy".
"The "Hijab Day" group singled out Valls on their Facebook page, suggesting that he saw the headscarf as "a battle at stake" for France.