Strict new government scrutiny on Chinese people who want to convert their money into other currencies threatens to slow the rush of foreign property buying that has stoked sky-high home prices around the world.

For months, China has sought to dam the flood of money pouring out of its borders, which has rapidly diminished its stockpile of foreign reserves. It has raised new barriers to companies buying abroad and moving money out of the country. Now, authorities here are taking new steps to bar…