Applications from across the European Union have already dropped by 14% at Cambridge University for undergraduate courses, MPs were told.
Hostility towards immigrants, devaluation of the pound and uncertainty over research projects have also deterred postgraduates from heading to the UK, the Education Select Committee was told.
Quitting the EU provides opportunities to improve research funding and international collaboration but a so-called hard Brexit would be damaging for the sector, academics said.
Alistair Fitt, vice-chancellor of Oxford Brookes University, said: “It would probably be the biggest disaster for the universities sector in many years.”
John Latham, vice-chancellor of Coventry University, said it would make British universities “extremely uncompetitive”.
Catharine Barnard, EU law professor at the University of Cambridge, said: “It promptly cuts off the flow of excellent people who are coming at the moment.”
Prof Barnard said there had already been a drop in EU student applications.
“This year we have seen at Cambridge a 14% reduction in the number of applications from the European Union at undergraduate level, although I should say the number of applications from EU students at postgraduate level are up,” she said.
“In respect of those who have declined an offer from Cambridge at postgraduate level, we have put a question in the so-called decliners survey to say ‘what was it that dissuaded you from coming?’
“Those who answered the question offered a range of factors from a concern about anti-immigrant sentiment to devaluation of the pound and the fact that their scholarships would be worth less, although obviously not in the UK, and uncertainty over future research collaboration.”
Prof Fitt told MPs the UK does not “get as much out” of some research and innovation funding pots as it puts in.
He said: “European structural funding is very important for the UK but the UK, I believe, doesn’t get as much out of it as they put in.
“Structural funding can also come with quite a few strings attached, can come with quite a few risks and can be quite hard to manage.
“So, if we were able to replace the amount of structural funding with our own funds, that’s a real opportunity that we could not only retain all that’s best in that system, but actually make it an even better system.”
Alastair Buchan, head of Brexit strategy at the University of Oxford, said the sector had been hit when Britain joined the EU.
He said: “One of the things that we did lose was that nice and easy flow of clinicians and clinician science from Canada, the US, Australia, New Zealand and South Africa.
“We had really good collaborations, which hopefully in this Brexit climate might be reinvented, because that movement of English-speaking medicine was actually a casualty of joining Europe.”
Oxford is setting up a Brexit observatory to collect data on the impact of quitting the EU, he said.
Engineering Professors’ Council president Stephanie Haywood said Britain would still need to employ thousands of engineers from Europe to fill the gap of 40,000 graduate staff in the industry.
“We’re doing lots of things to try to encourage more people to take up physics and STEM subjects, we’re trying to get more women into engineering, but I don’t see these things being very quick fixes and I think it’s going to be very difficult to fill the gap other than by recruiting engineers from overseas, and that includes the EU.”
Prof Haywood also pointed out that only 30% of PhD students in engineering are British and the industry is “heavily reliant” on postgraduates filling high-end jobs.
The uncertainty over the status of EU nationals post-Brexit is causing many postgraduates to consider moving abroad, whether they are from Europe or have spouses from the continent, she said.
Anne Corbett, an associate at LSE Enterprise, called on ministers to take action to halt any potential “brain drain”.
Dr Corbett told MPs: “I think that the issue we’re talking about here is actually one which requires Government intervention and it requires it before the negotiations start.
“I would say that were the Government to come out of its kind of purdah, or whatever it’s called, and say that from the start it would be creating a much more positive climate, to assure that EU citizens here were safe, which in the end is helpful all round.”