European students applying for UK degrees in 2017 need guarantees about funding or their numbers could crash, university leaders will hear later.
EU students currently pay the same fees and have the same access to loans as UK students.
But those starting in 2017 and 2018 could lose out after Brexit, Universities UK president Dame Julia Goodfellow will warn in a speech.
Ministers should provide urgent reassurance, Dame Julia will say.
Following the EU referendum in June all four UK nations confirmed that current EU students and those starting courses this autumn would be eligible for loans and grants to fund their studies for the duration of their courses.
But there has been no such clarification for EU students applying to start degrees next year or the year after.
The Brexit process is likely to take at least two years, so these students could face changes to fees and funding during their courses, and this could put them off applying to UK universities, Dame Julia will argue.
The application process for degrees starting in 2017 opened on Tuesday so the situation has now become urgent, she will warn the Universities UK annual conference in Nottingham.
She wants the UK government to take “swift and positive action” to reassure EU students applying for next year that they will pay the same fees and have access to the same financial support throughout their courses.
This is necessary to “prevent a likely sudden decline in EU student applications” across the UK, she will warn.
Currently more than 125,000 EU students are studying at UK universities, about 5% of the overall student population, Dame Julia, who is vice-chancellor of the University of Kent, will say.
“Put simply, universities are currently unable to answer two crucial questions that are being frequently asked by prospective EU students considering whether to apply to start courses in the UK in autumn 2017: ‘What fees will you charge for any years of my course which are post the date of exit?’ ‘Will I be able to access any financial support?’
“This issue is urgent. Ucas applications opened yesterday for the 2017-18 intake and EU students are almost twice as likely as UK students to apply very early for those courses with October deadlines.
“I urge government to take swift and positive action to address uncertainty, prevent a likely sudden decline in EU student applications and provide much needed reassurance to prospective EU students and universities across the UK.”
Dame Julia’s warnings follow concerns about the stability of research funding at UK universities, with some research groups saying they lost out on grants in the weeks following the referendum.
The latest global university ranking table, published on Tuesday by QS, shows UK universities losing position compared with international competitors.
“Uncertainty over research funding, immigration rules and the ability to hire and retain the top young talent from around the world seems to be damaging the reputation of the UK’s higher education sector,” said QS head of research Ben Sowter.
Mr Sowter said his research was carried out before the referendum but he believes the result will have “undoubtedly added to this uncertainty”.
A Department for Education spokesman said: “EU students make an important contribution to our world-class universities, and we want that to continue. While the UK remains a member of the EU, rules regarding the student loans EU nationals receive are unchanged – EU students currently eligible to receive funding will continue to do so for courses they are currently enrolled on, or about to start this autumn.
“The government will continue to work closely with the sector.”