CIUDAD JUÁREZ, Mexico—A surge of Cuban asylum seekers, long accustomed to preferential treatment under U.S. migration policies, are being stopped by U.S. government efforts to contain a tide of Central Americans migrating north.

Thousands of Cuban migrants have been stranded for months in violent towns along the U.S.-Mexico border, trying to request asylum in the U.S. even as the Trump administration imposes more restrictions on asylum seekers.

In...