The motion was tabled after Andrew's interview with the BBC, broadcast on Saturday evening, in which he discussed his links to billionaire paedophile Jeffrey Epstein.
The president of Huddersfield Students' Union, Emmanuel Haruna, said: "As part of our processes to give students a voice, a student has put forward a motion to lobby Prince Andrew to resign as chancellor."
The motion was discussed by the termly student panel at 5pm on Monday, and the outcome is due to be published in the next few days.
Speaking to BBC Radio 4's PM programme, a former Huddersfield University lecturer Stephen Dorril added: "It's [the duke's link to Epstein] unacceptable and damaging the reputation of the university.
"Students are very concerned, certainly during my time there, about things like sexual harassment and Me Too movement, and to be associated with someone who at the very least was a friend of a convicted sex trafficker and paedophile, is not a good thing for the university."
It comes as the university released an official statement in support of the duke.
A spokesman said Andrew had "long ties" with the university and "his enthusiasm for innovation and entrepreneurship is a natural fit with the work of the university".
They had "nothing further to add" in relation to the allegations after Buckingham Palace's emphatic denial of any wrongdoing.
Andrew was made chancellor of the university in July 2015.