The union is supporting a campaign to stop Bangor University student Shiromini Satkunarajah being deported to Sri Lanka.
The 20-year-old has been taken to a detention centre after being refused asylum.
The Home Office said it considers each case carefully.
Miss Satkunarajah, who was born in Sri Lanka but has lived in the UK for eight years, is due to finish her electrical engineering degree this summer.
She was arrested on Tuesday and taken to a detention centre to await deportation on 28 February.
Thousands of people have signed a petition to stop her deportation.
NUS Wales deputy president Carmen Smith told BBC Wales: "We want the home secretary to stop the callous and inhumane deportation of Shiromini.
"She doesn't have any family or friends in Sri Lanka. Wales is her home.
"She has three months left of her degree. It's a brutal thing to do at such a time in her educational experience."
Arfon MP Hywel Williams said the UK government should use "common sense" in dealing with Miss Satkunarajah's case.
"She has three months to go before she graduates in a field where we really do need people and she's an excellent student," he said.
"There is a certain amount of discretion they can operate and I really wish they would."
A Home Office spokeswoman said: "We do not routinely comment on individual cases.
"The UK has a proud history of granting asylum to those who genuinely need it and every case is carefully considered on its individual merits."
Any student seeking asylum should be able to finish their education here, the National Union of Students (NUS) Wales has said.