One of the country's largest for-profit education companies warned Thursday that it may have to shut down after the Obama administration moved to restrict the company's access to federal funding.

Corinthian Colleges Inc., which operates Everest College and other schools, has about 72,000 students who receive roughly $1.4 billion in federal financial aid each year. But the company and its for-profit rivals, which enroll about 13% of the nation's higher-education students, are drawing greater scrutiny from regulators over concerns...