The EU has suspended talks with Switzerland over its participation in EU research and education programmes because of the Swiss vote last week to curb immigration.
Switzerland's access to millions of euros of EU funding is now at risk.
A European Commission spokesman said the Horizon 2020 research programme and Erasmus+ student exchanges were linked to freedom of movement.
Switzerland has blocked free access to its employment market for Croatians.
Switzerland is not in the EU but more than half of its exports go to the 28-nation bloc and it has adopted large sections of EU policy.
Integration with EU
Horizon 2020 will provide nearly 80bn euros (£65bn; $110bn) over seven years for research projects in the EU.
In the current programme Swiss participants have received more than 1.8bn euros in research grants. The first new grants are to be decided later this year.
Erasmus+ has a budget of 14.7bn euros and enables more than four million young Europeans to study and get work experience abroad.
Like most EU member states Switzerland is also in the Schengen zone, which enables citizens to cross European borders without passport checks.
When Croatia joined the EU last summer Switzerland agreed to grant Croatians the same rights as those enjoyed by other EU workers in Switzerland.
But at the weekend Switzerland said the accord could not be signed "in its current form", after an 8 February referendum invalidated the Swiss-EU pact on freedom of movement.
Swiss voters narrowly backed a proposal to bring back strict quotas for immigration from EU countries.
Referring to Horizon 2020 and Erasmus+, the EU's envoy to Switzerland, Richard Jones, said "there is a link between these agreements and freedom of movement".
In a comment to the AFP news agency, EU Commission spokesman Joe Hennon said that "given the circumstances and in the absence of a clear political signal to do so, upcoming negotiation rounds have been postponed until Switzerland signs" the Croatia deal.
Last month the EU Science Commissioner Maire Geoghegan-Quinn praised Switzerland for its success in winning EU research grants.
Ms Geoghegan-Quinn said Swiss research was especially strong in the areas of computer science, health, nanoscience and new production technologies.
Although the Swiss economy is booming and unemployment is low, many Swiss worry about the effects of immigration.
Geraldine Savary, a senior Swiss parliamentarian and socialist, said suspension of Swiss participation in Horizon 2020 would be a "catastrophe" for the country's research, because Switzerland "receives much more today than it puts in".
Speaking to the Swiss public broadcaster RTS, she said that for at least two years "researchers won't be able to submit projects". Swiss scientists in Lausanne and Zurich participating in the EU's Human Brain Project would be among those affected, she warned.
Ms Savary is a science specialist in the Council of States, the Swiss upper house.
Blow to Croatia
Earlier Justice Minister Simonetta Sommaruga called Croatian Foreign Minister Vesna Pusic to tell her Switzerland would not be able to sign the deal extending the right of free access to Switzerland to the EU's newest member state.
Ms Sommaruga also informed Brussels that the agreement needed to be re-examined, her spokesman Philippe Schwander said.
The Swiss referendum had created a "new constitutional disposition", Mr Schwander noted.
He stressed that the justice minister was seeking a "solution" to ensure Croatians were not being discriminated against.
Following the vote, the EU warned it would reassess its relations with Switzerland "as a whole".
A quarter of Switzerland's eight million-strong population is foreign, and last year 80,000 new immigrants arrived.
Since 2007, most of the EU's 500 million residents have been on an equal footing with locals in the Swiss job market - the result of a policy voted into law in a 2000 referendum.
But a coalition led by the right-wing Swiss People's Party has pushed to reverse this deal, calling it "a huge mistake".
Supporters of quotas believe free movement has put pressure on housing, health, education, and transport. They also argue that foreign workers drive salaries down.
The Swiss government and business leaders say free movement is key to Switzerland's economic success, allowing employers to choose skilled staff from across Europe.
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