WASHINGTON—The number of visas issued to foreign students fell markedly last year amid stricter immigration policies, State Department data show, exacerbating financial challenges for some U.S. colleges and universities.

Some of the slide can be attributed to stepped-up competition from schools in other countries and less support for foreign study by some governments. But immigration attorneys and school officials say Trump administration policies are making the U.S. a tougher destination for foreigners and point to stricter scrutiny of those who do apply.

In the year ended Sept. 30, 2017, the State Department issued 393,573 student visas, known as F-1s. That was down 17% from the previous fiscal year and nearly 40% below the 2015 peak. The drop-off was particularly dramatic among Indian students this year, with a 28% decline in visas from the second-biggest feeder of foreign students at U.S. colleges.

There was also a big drop from China—down 24% last year and the No. 1 source of foreign students in the U.S.—but much of that reduction can be traced to a 2014 change in visa terms for Chinese students. Their visas are now good for five years, instead of one, meaning there are fewer visa renewals but not necessarily fewer students.

There were about 78,000 fewer visas issued in fiscal year 2017 compared with 2016 for all countries, including about 35,000 fewer from China. Setting aside visas from China, the overall drop in visas issued was 13% from 2016 to 2017.