He spoke out after Exeter university decided to close its chemistry department to save money, provoking complaints from scientists and students.
Nobel prize-winning scientist Sir Harry Kroto said he would return the honorary degree he received from Exeter in protest at plans to close its chemistry department.
"It was an honour from a university that at the time recognised that chemistry was one of the major subjects," he told BBC Radio 4. "If it decides that it no longer has that, and it is not a priority, then I don't wish to have an honour from that university. It's as simple as that."
Mr Clarke has sent a list of courses that Cabinet ministers believe universities should offer to David Young, chairman of the Higher Education Funding Council for England (HEFCE). In it, he asked for advice on how to keep the subjects alive and said plans were afoot to see what "intervention" was needed to protect them.
Mr Clarke said: "Any sensible government needs to take a long-term view of what students are studying and whether we have enough graduates in the subjects needed to help our economy and society thrive. That is why I consulted Cabinet colleagues over the courses they felt needed extra protection.
"We have now agreed a list of key subjects of national strategic importance.
"The list includes minority languages, science, technology, engineering, maths and vocationally-oriented courses of particular interest to employers in areas of growing importance to the UK economy.
"I have asked the HEFCE to report to me on whether we are doing enough to protect them all, and what intervention might be right for those courses that need protection. Specification of these particular subjects does not mean that they are more important than others.
"But they have been pinpointed because there are particular concerns that on current trends we may not be able to produce enough graduates in these fields in the future, and have them provided for in enough regions across the country."
Plans to close Cambridge university's architecture department attracted 1,000 architects to a demonstration outside Senate House in Cambridge this week.
The protest was backed by the prize-winning architects Sir Richard Rogers and Sir Norman Foster.