Scots “honours” degrees last four years and Home Secretary Sajid Javid is being urged to “immediately” act to tackle the situation to make sure Scots universities are treated the same as those elsewhere in the UK.
University leaders are warning the European Temporary Leave to Remain (ETLR) scheme, being propose under a no-deal Brexit scenario, would discriminate against Scottish universities.
Students wanting to study engineering and medicine courses, which last more than three years UK-wide, would also be hit.
Universities in Scotland attract more than 25,000 students from across Europe each year.
Edinburgh South MP Ian Murray has stepped up calls for action in a letter to the Home Secretary penned along with East Lothian MP Martin Whitfield.
“Universities in Scotland conventionally offer honours degrees that last a period of 48 months, therefore longer than the leave to remain protocol allows,” their letter states.
“Studying over a period of four years is a historic custom of Scotland’s education system.
“Four-year degrees allow students to broaden their expertise and grow as undergraduates over a longer duration of time.
“The impact of limiting temporary leave to remain to 36 months means that skilled EU students may be deterred from applying to Scottish universities. This would disadvantage our universities and affect the world-leading research they undertake.”
Universities contribute more than £11 billion to the Scottish economy annually and support more than 40,000 direct jobs.
The Scottish Government’s higher education minister Richard Lochhead warned the policy threatened the ability to “attract and retain” EU staff and students.
“The UK Government’s immigration policy ignores the fact that the majority of undergraduate courses in Scotland last four years,” he said.
“It must be dropped immediately. I will raise this with the UK Government at a meeting of education ministers tomorrow.
“More generally, this is just a further example of how Scotland’s distinct and specific needs have been totally ignored by the UK Government throughout the entire Brexit process.”
Alastair Sim, director of Universities Scotland, warned the sector would suffer “disproportionate damage” under the proposals and said the situation must be rectified.
“In the event of a no-deal, the proposal means EU students due to start their courses this September will have to apply for European Temporary Leave to Remain and then switch to a study visa to complete their final year,” he said.
“This burdensome process, which also incurs costs for the applicant, could discourage prospective students from coming to the UK.”
Liberal Democrat deputy leader Jo Swinson urged the Home Office to address the situation.
“The Scottish university system is a world leader in part because it attracts students from all over the globe who enrich our culture and help grow our economy, but the Government’s new visa plan risks damaging that reputation,” she said.
The Russell Group, which represents the UK’s leading universities, claimed the scheme “backtracks” on commitments that any EU citizens arriving before the end of 2020 would be eligible to apply for settled status.
The Home Office has said there were no limits on the number of international students who would be allowed to study under a no-deal scenario.