A vote to leave the EU in the UK's 23 June referendum would also "cripple" cross-border collaboration in the education sector, warns the European University Association (EUA).
The Brussels-based association is the representative organisation of more than 800 universities in 47 European countries and 36 national rectors' conferences (NRCs).
There are particular concerns about the impact a Brexit could have on the successful Erasmus programme.
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This is a student exchange programme, named after a Dutch philosopher, established in 1987. It enables students and many young people to study in another European country.
Erasmus Plus, the new programme combining all the EU's current schemes for education, training, youth and sport, was started two years ago.
In the past 20 years, over three million students have benefited from Erasmus grants.
But, speaking exclusively to the Parliament Magazine, EUA Secretary General Lesley Wilson, has sounded a dire warning of the potential impact of a Brexit on education.
She told this website, "A British exit from the EU would be a disaster for universities and leave them struggling to compete on the European and world stage, making recruiting and retaining talent harder and crippling the cross border collaboration, for example through the EU's ERASMUS and H2020 programmes, on which the higher education and research community thrives."
Her concerns were echoed by former British Liberal Democrat MEP Andrew Duff, who told this website, "EU membership has enabled British universities to recruit some of the very best scholars and students from other European countries."
Duff, President of the Union of European Federalists, added, "My own university of Cambridge would not be at the top of world league tables if it had not exploited to the full all the academic and financial advantages of being first and foremost a European and not merely a British university. Staying in the EU and building on that European legacy is what matters now."
A recent report by Greens/EFA group MEP Ernest Maragall said that Erasmus Plus "can be part of the answer" to the current economic and social problems in different European countries and reduce rates of youth unemployment by “building strong links between education and training and employment.”
Elsewhere, the Brexit campaign has intensified with the respected think tank Breugel publishing research on the profile of immigrants to the UK.
Zsolt Darvas, from the Brussels-based group, writes that the bulk of immigrants from 2008-2014 were 20 to 30 years old, and many of them are in work.
Meanwhile, a survey by Ipsos Mori suggests 58 per cent of Italians and 55 per cent of the French want a referendum on the EU and that 48 per cent of Italians would like to even bid farewell to the EU.