Of 1,763 would-be students who had contacted or applied to UK universities, almost half said Brexit would make UK study less attractive.
But 17% told international student recruiters Hobsons that Brexit would make UK universities more attractive.
The Vote Leave campaign said it was crucial to ensure there were enough places for young people from the UK.
Hobsons managing director Jeremy Cooper said: "A vote for Brexit would represent a further challenge.
"For universities in the UK, the conditions for recruiting international students are tougher than ever before."
The survey participants had applied for or enquired about study at 15 UK universities - including two from the elite Russell Group and seven new universities.
Three-quarters were from countries outside the EU, two-thirds were interested in post-graduate study, just over half were female and almost two-thirds were aged under 24.
Of the 1,529 who expressed an opinion:
There was considerable variation between EU and non-EU students, with 82% of EU students saying Brexit would make the UK less attractive compared with 35% of non-EU students.
Although they admit accurate predictions are impossible, the researchers believe international student applications could be at risk if attitudes change as the survey suggests.
Based on 2014-15 figures, when there were 240,767, international students in the UK, 113,116 international students "could be at risk of being put off" studying in the UK, says the report.
It suggests the UK could potentially lose 50,056 EU and 63,060 non-EU students.
Paul Blomfield MP, co-chairman of the newly formed all-party parliamentary group for international students, called the report "worrying"
"Leaving the EU would make the UK a less attractive destination for study, and that is bad news for our economy," he said.
"Across the country, hundreds of thousands of jobs would be at risk."
His co-chairman, Lord Bilimoria, said the findings were consistent with views he had been hearing from around the world.
"It is not scaremongering," he said. "It is reality. The whole world thinks we should stay in the EU.
"International students are one of our biggest most important export earners.
"They affect our economy and our soft power - building bridges with our country for generations."
Nicola Dandridge, chief executive of Universities UK, warned that "leaving the EU and putting up barriers to work and study are highly likely to mean that international students choose to study elsewhere, strengthening our competitors and weakening the UK's universities".
But a Vote Leave spokeswoman pointed out that only a small percentage of students from outside Europe believed the referendum result would make any difference to their opinion of the attractiveness of studying at a UK university.
"The UK has some of the best universities in the world and gaining a place is often extremely competitive. That's something we're rightly proud of as a country.
"Understandably, the calibre of our universities attracts a large number of applications from foreign students - but arguably the most important thing is to ensure that there are sufficient places for our young people."
And a spokesman for Scientists for Britain noted "a huge difference between the 'UK study less attractive' response from non-EU students (35%), who contribute up-front and pay higher tuition fees, and EU students, who pay lower fees and are eligible to access UK student loans".
"Given that the financial contribution of non-EU students is significantly more important to the UK Higher Education sector, we are reassured that the vast majority of non-EU students (65%) recognise that Brexit is much less of a concern for them, and may even level the playing field in terms of being able to secure student visas to study in the UK."
UK universities could find it harder to recruit international students if the UK leaves the EU, suggests a survey.