The decision lets the Trump administration halt, for now, a program that lets migrants from Cuba, Haiti, Nicaragua and Venezuela live and work in the U.S. for up to two years.

The Supreme Court on Friday stayed a lower court order that blocked the Trump administration from deporting roughly 500,000 migrants from Cuba, Nicaragua, and Venezuela.

“It’s chaotic and unnecessary, and we’re already receiving panicked calls and emails, and the crescendo will only grow,” said Karen Tumlin, founder and director of Justice Action Center, an immigrant...