Foreigners seeking permanent residency in the US will now have to leave the country to apply for green cards, a change with potentially far-reaching ramifications for legal immigration amid President Donald Trump’s sweeping crackdown.

Most applicants already living in the US will now have to leave the country and apply from their home nations.

While there are approximately 1.5 million Indian Green Card holders in the US, an additional 1.2 million highly skilled Indian nationals and their dependents are estimated to be presently stuck in the...