The Republican lawmaker from Florida calls their recent trip "hypocritical" and he takes issue with the U.S. government's approval of the visit as a cultural mission.
Beyonce and Jay-Z marked their wedding anniversary in Havana last week.
U.S. citizens aren't allowed to travel to Cuba for mere tourism, though they can obtain licenses for academic, religious, journalistic or cultural exchange trips. These people-to-people licenses were reinstated under the Obama administration.
Rubio, a Cuban-American, says such trips provide money to the Castro government to oppress the Cuban people.
Rubio discussed the trip during interviews Sunday on CNN's "State of the Union," ABC's "This Week" and NBC's "Meet the Press."