New figures show the total of EU students increased by 7% in 2011/12 – from 16,310 to 17,475.
Under EU legislation, the £75 million cost of educating such students is the responsibility of the Scottish taxpayer.
Because the amount of money the Scottish Government spends on higher education is capped, any dramatic increase in EU students would mean fewer places for Scots.
The additional pressure has been caused by the introduction of tuition fees in England of up to £9000, making Scotland a much cheaper option for EU students.
The Scottish Government increased places to ensure no Scots missed out last year, but future rises could threaten the status quo.
Education Secretary Michael Russell has raised the prospect of a service charge for EU students to redress the balance, but there has been little progress to date.
Hugh Henry, Scottish Labour's education spokesman, said the increase in EU student numbers would mean more subsidies from the Scottish budget and, therefore, cuts elsewhere.
He said: "It looks like this SNP Government is prepared to inflict savage cuts on essential services in order to provide free tuition to European students.
"This is a ticking time bomb which will inflict untold damage on public services in Scotland.
Liz Smith, education spokeswoman for the Scottish Conservatives, added: "For every EU student there is more pressure on the Scottish taxpayer.
"A multinational student body enriches Scottish higher education, but it has to be managed and funded sensibly."
However, Graeme Kirkpatrick, vice president of NUS Scotland, warned against any attempt to discourage EU students from studying in Scotland.
He said: "EU students studying at our colleges and universities are excellent ambassadors for Scotland, and the numbers enrolling in higher education are a clear sign of our continued status as a global education leader.
"We must remain a welcoming destination for EU students, and not take action that would risk us losing out on talented students who bring Scotland huge educational, cultural and economic benefits.
"Scotland also benefits when our students study elsewhere in the EU and our research has found studying abroad not only makes for a fantastic learning experience, but makes students more employable by bringing back new skills our economy needs."
A Government spokeswoman said: "Scottish student numbers continue to rise. We have increased the number of available places and announced a further 2000 places for 2013/14.
"While applications to Scotland from EU students were up just over 6% last year, acceptances increased by only half that amount. However, we will continue to work with universities to continue to ensure Scottish students have access to the opportunities they need."
Alastair Sim, director of Universities Scotland said: "We understand the Scottish Government is continuing to work with the European Commission to examine how it might be possible to see students domiciled in the rest of the EU make a fair contribution to the costs of their Scottish university education.
"We would be very interested in any progress on this front."