Hungary's new Higher Education Act means one of the country's leading universities, the Central European University in Budapest, will be unable to award diplomas because it is registered in the United States.
The Hungarian government says the legal change is needed to prevent foreign universities from issuing dubious diplomas.
But the European Union's executive Commission says the law undermines academic freedoms and democratic values.
European Commission Vice President Valdis Dombrovskis says Hungarian authorities have a month to respond to the Commission's formal notice.
"A letter of formal notice is a first step towards infringement procedure but there is a time for Hungarian authorities to react to the letter of formal notice and then, following the reactions, the Commission will decide on further steps."
Under the new legislation, those working at the Central European University will in future require work permits, which the institution says will limit its ability to hire staff.
The government has also demanded that the university open a campus in the United States, and that it no longer teach US-accredited courses.
The European Commission says the measures breach the University's right to exist and serve its students.
Hours later Hungarian Prime Minister Viktor Orban responded at the European Parliament in Brussels, saying the claims are "groundless".
"We would like to stress that nothing threatens the existence of the Central European University. The University will continue its operations under all circumstances. This accusation is groundless, it has no basis in fact. The situation is absurd, it is like someone being accused with murder and sentenced for it while the victim of the purported crime is alive and kicking; moreover, points at the convicted, crying 'murderer'."
The latest feud between Hungary and the EU marks a new low in the tense relations between Brussels and Budapest over the Hungarian government's rights record.
Mr Orban has often clashed with the EU, and has now attacked Non-Government Organisations sponsored by Hungarian-born billionaire George Soros.
Mr Orban accuses Mr Soros, who founded the Central European University after the fall of the Berlin Wall, of destroying millions of lives.
"Although George Soros ruined the lives of millions of Europeans with his financial speculations, although he was fined for speculation in Hungary, and who is an open enemy of the euro, he still is so valued here that the top leaders of the European Union receive him."
Mr Orban has also clashed with deputy Commission head Frans Timmermans.
Mr Timmermans says there are ongoing concerns about Mr Orban's stance on asylum-seekers, his bid to tighten rules on NGOs and the rights of the Roma.
"The biggest, single biggest miracle in my lifetime is the fall of the Berlin Wall, the fall of the Iron Curtain and that Hungary became one of the democratic nations of Europe and that is not something, that is not something the European Union should claim credit for. This is something that was done by the Hungarian people themselves, striving for freedom. Protecting their freedom, however, is now a common European task and we will have to fight for that."
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