The Trump administration blocked Major League Baseball from signing players directly from Cuba to play professionally in the U.S., nullifying a historic deal the league struck in December with the island nation’s baseball federation.

The move comes amid a broader crackdown on what the administration calls the “Troika of Tyranny”—Cuba, Venezuela and Nicaragua. The Trump administration has criticized Cuba for supporting Venezuelan dictator Nicolás Maduro, and has sought to curb some of the normalization of U.S. relations with...