The Home Secretary accused universities of being complacent in tackling the radicalisation of students on their campuses.
“I think for too long there’s been complacency around universities,” she told the Daily Telegraph.
“I don’t think they have been sufficiently willing to recognise what can be happening on their campuses and the radicalisation that can take place.
“I think there is more that universities can do.”
Mrs May warned that funding would be cut to Islamic groups which espouse extremist views.
Her comments come ahead of the release on Tuesday of the Government’s revised Prevent counter-terrorism strategy.
Particular concern is believed to have been expressed over the Federation of Student Islamic Societies.
“They need to be prepared to stand up and say that organisations that are extreme or support extremism or have extremist speakers should not be part of their grouping,” Mrs May said.
The Daily Mail reports that the Government has identified 40 English universities where there could be a “particular risk” of radicalisation or recruitment on campus.
Mrs May has drawn criticism for her comments.
Jeremy Clines, Anglican chaplain at the University of Sheffield, said the serious problem facing universities today was not radical Islam but university spending cuts.
“People will explore radical views whether they are at university or not,” he said.
“Universities are fantastic places for people to learn from each other and, contrary to the notion that they foment extremism, can help to moderate extremist views by encouraging dialogue and understanding, and by providing opportunities for people to explore views that are different from theirs.
“In that sense, they are a great place for developing community cohesion.”
The Student Christian Movement warned against exaggerating the problem.
"SCM opposes groups who promote violence and bigotry, whether they be Muslim, Christian or anything else," it said in a statement.
"We should not imagine that such tendencies are confined to Muslims. Christian students across Britain engage in constructive dialogue with Muslims, people of many other religions and those of no religion.
"They work together where they agree and debate with respect when they do not. SCM is concerned that talk of 'radicalisation' risks exaggerating the problem posed by extremist speakers and fuelling the fear and division from which extremism grows."
President of the National Union of Students, Aaron Porter, accused Mrs May of “wild sensationalism” and of seeking to shift the blame for extremism onto universities.
“Given that the law requires universities to provide freedom of speech, and the government refuses to ban the hardline group Hizb ut-Tahrir despite promises to do so, it appears irresponsible of Theresa May to try to shift the blame for non-violent extremism on to universities or students,” he said.
"Facing up to the challenges that non-violent extremism brings to campus life requires careful support and guidance from government, not wild sensationalism that only serves to unfairly demonise Muslim students."