New official figures show that universities and other sponsors of international students reported at least 27,121 non-EU students to the UK Border Agency in the 18 months leading up to August last year.
As part of new rules to tighten the students visa system and prevent its abuse, academic staff are required to report to immigration authorities if non-EU students are absent from classes or if their activities arouse suspicion.
The Universities and College Union said "pressure on staff to spy on their students" would create an environment of mistrust on campus and risked jeopardising the crucial relationship between staff and students.
Universities and colleges are now required to report suspicious or bogus students or risk being stripped of their licence to sponsor students from outside the European Union, who pay more than three times the fee paid by UK students.
The union said the news that thousands of foreign students are being reported to immigration officials each year could make the UK a less attractive place to study for overseas students.
UCU general secretary, Sally Hunt, said: "The relationship between staff and students is an incredibly important one that is built on trust. Fears that lecturers are spying on students, whether they are or not, risks jeopardising that relationship".
She added: "Successive governments have seen plans to turn lecturers into spooks overwhelmingly rejected by the academic community and we will continue to oppose such moves, which would make the UK a less attractive proposition to foreign students."
The Manifesto Club campaign group, which obtained the figures of non-EU students being reported to immigration authorities, said the stringent visa controls were forcing UK academics to spy on their own students, eroding academic autonomy and damaging relationships between students and staff.
In its Students Under Watch report, the group said: "Universities are reporting large numbers of international students to the UKBA.
The agency asks sponsors to email any suspicions about students; each notification can include information about several students."
International students are a crucial source of revenue for cash-strapped British universities. Every year, thousands of students from India and other non-EU countries enroll on courses in universities and colleges here.
The Home Affairs Select Committee has warned that the David Cameron government's reforms aimed at cracking down on abuse of the visa system could cost the economy £3.6 billion in a "worst-case scenario", including loss of tuition fees and visa fee income, as well as a reduction in students and their dependents able to come to the UK.