If it happened to Harvard University, could it happen anywhere?

The Trump administration’s surprising bid to end Harvard’s international enrollment put the higher education world on edge this week, looming as a larger threat against academic autonomy.

Well beyond the halls of Harvard this week, college leaders were shocked that one swift move by the federal government could eliminate their ability to serve students from abroad, a growing population that has infused their campuses with cachet and wealth.

“This is a grave moment,” Sally Kornbluth, the president of the Massachusetts Institute of Technology, wrote in a message to her campus.

More than 5,000 miles away, Wendy Hensel, the president of the University of Hawaii, said that it was “reverberating across higher education.”

President Trump has already unnerved universities this year by launching investigations, freezing grants, demanding changes in campus practices and attempting to deport international students. He has justified his punitive approach as a means to combat what he considers antisemitism. But he and his allies also have long resented a perceived liberal bias and racial diversity efforts at prestigious colleges.

The Trump administration said Thursday that it revoked Harvard’s international student certification because the university had failed to meet its demands, including a request for records of student protest activity dating back five years.