The former universities and science minister attacked the plans in a Times opinion piece on 23 December.
He argued that the UK should be increasing its share of the overseas students market, warning that “if we implement the latest idea from the Home Office for new restrictions on overseas students, we would not only miss this golden opportunity – we would be acting in a mean-spirited and inward-looking way”.
Ms May wants the next Tory manifesto to include plans to force overseas students to leave the country once their courses have ended, with universities responsible for ensuring they depart, according to a Sunday Times story based on briefings from a “source close” to the home secretary.
Her plans have been condemned by the Liberal Democrats, by a Financial Times leader and by Universities UK.
Lord Bilimoria, the Indian-born University of Birmingham chancellor and founder of Cobra Beer, called Ms May “more dangerous” than Nigel Farage, the UK Independence Party leader.
The former overseas student at the University of Cambridge warned that her policy would “cause untold damage to our universities and to the British economy”.
Newspapers in India – a key source of overseas students for UK universities – have reported on Ms May’s plans, leading to concerns that her move has already further damaged the standing of British higher education overseas.
“UK to ‘kick out foreign graduates’ to curb immigration,” was the Times of India headline.
“Come to the UK: Graduate, and then get the hell out!” was the Bangalore Mirror take on Ms May’s plans.
Mr Willetts said that higher education “is an export market with massive opportunities for us”, adding that it is “already our second biggest export to China”.
He argued that reducing overseas student numbers “does not match the public anxiety about immigration”, adding that he had never heard complaints from voters about “Chinese students studying physics. That is not the problem.”
Mr Willetts continued: “If we must target immigration as measured by the number of people here for more than a year I would instead look at the other side of the balance sheet.” He called for more measures to increase the number of British students studying abroad.
Lord Bilimoria said: “The home secretary is sending a message of hostility to the world’s brightest and best just at the moment when Britain’s businesses are suffering from severe skills shortages.
“Theresa May’s statement is economically illiterate and the fact that she is a member of Cabinet makes her even more dangerous than Farage and his party’s extremist scaremongering. The Prime Minister should speak out against the home secretary’s comments and make it clear that our universities and our economy welcome talented individuals from around the globe.
“Today I see my Indian beer drunk in pubs across Britain. That would never have happened if I hadn’t been given a chance to contribute after I graduated from Cambridge.”
