Education Minister Leighton Andrews says the University of Wales has let down higher education in Wales and brought the nation "into disrepute".
His criticism comes after a watchdog's report told the university to review its worldwide college links.
BBC Wales found the links included one with a Malaysian pop star with bogus degrees and a college in Bangkok college said to be operating illegally.
The university says it is developing a new international strategy.
Prof Roger Brown, a higher education expert, said it was the "most damning" report on a university's overseas operations he had seen.
The Quality Assurance Agency (QAA) delayed its publication of the university's institutional review - a six-year health check - while it conducted its investigations.
The institutional review was completed before BBC Wales' revelations were broadcast and reached judgments of 'confidence' in the university, although it did identify weaknesses in its external validation processes.
The university must now draw up an action plan to address the issues.
The QAA's investigation follows the BBC Wales probe into colleges in Malaysia and Thailand offering courses leading to the university's degrees.
Last November BBC Wales Week In Week Out found that a Malaysian college was run by Fazley Yaakob, a pop star with two bogus degrees, while another in Bangkok was operating illegally.
The QAA's report found the university had not run proper checks while setting up partnerships with the colleges in question - a process known as validation.
It said the university "missed the opportunity to be circumspect" about Mr Yaakob, who claimed to have a doctorate in business administration.
Its approval of a fashion college in Thailand was judged "inadequate" and "flawed".
The QAA investigation revealed that the University of Wales staff member sent to inspect the college had no recollection of being there.
The report also considered the university's links with a business college in Singapore in which two sets of owners disappeared, leaving students in the lurch.
Mr Andrews told BBC Wales: "The university has brought the brand of Wales into disrepute and I think it has let higher education in Wales down and it has let Wales down. It's unacceptable.
"There have been continuing concerns about the University of Wales' international operations, going back several years.
"I want to see action from the chair of the council at the university because all of this has happened on his watch.
"What is he doing about it and what is he going to do in the future to ensure that he exercises proper oversight of the management of the University of Wales."
In total, the university has 130 partnerships in 30 overseas countries, with 20,000 people studying for its degrees across four continents.
The outcome of the QAA investigation is the latest blow for the university, following the publication of a report in March which said it should be wound down and closed if other plans for its future fail.
The review, commissioned by the Welsh Government, said it had become too reliant on income from validating courses in overseas colleges.
The University of Wales is the degree awarding body for five institutions - UWIC, Trinity Saint David, Glyndwr University, Swansea Metropolitan and Newport.
However, according to the QAA, students at these universities are "commonly unaware of the university (of Wales) and believe themselves to be acquiring their degrees from the institution they have attended."
Cardiff, Swansea, Bangor and Aberystwyth have all withdrawn from the university in recent years.
Prof Brown said the university had "some very very serious issues to answer".
"It's a serious challenge and one the university has to address with the utmost seriousness if the university is to retain its reputation in this field.
"I have never heard of a case where the QAA has asked a university to review all its partnerships in such number, that is certainly unprecedented.
"I would say this is one of the most serious reports to have been produced on a university in recent years."
Prof Philip Gummett, chief executive of the Higher Education Funding Council for Wales (HEFCW), said the report identified "a considerable range of serious shortcomings" in the university's conduct.
"There needs to be an urgent and effective response," he said.
"We shall also take these developments into account in our consideration of current merger discussions involving the University of Wales."
The University of Wales said it welcomed the institutional review report's finding that confidence could be placed in the soundness of its management of the academic standards of its awards and the quality of learning opportunities available.
A spokesman said it was making "many transitional and transformative measures".
"In order to continue to safeguard standards and the student experience the University of Wales will, in partnership with its proposed merger institutions, develop a new international strategy which is embedded within Wales," he said.
Over the last six months there have been concerns expressed about the validation operations of the University of Wales.
The officers of the university have reviewed the validation activity and have come to the view that the current model is no longer fit for purpose and consequently has already imposed a moratorium on all validation developments.