U.S. enrollment of international students declined for the second year in a row, sending waves of unease across American colleges and universities, which see students from abroad as a buffer against the falling number of U.S. high-school students graduating each year.

The number of new international students enrolling at American institutions fell by 6.6% during the 2017-18 academic year, on top of a 3.3% decline the year before, according to a report by the Institute of International Education released Tuesday. The drop takes...