Jay-Z released a rap Thursday that said: "I turned Havana into Atlanta. Away from the hood, I got White House clearance. Obama said, 'Chill, you gonna get me impeached. You don't need this ... anyway, chill with me on the beach,'"
The United States restricts tourist travel to Cuba unless approved by the U.S. government and questions have been raised about the couple's visit.
"I guess nothing rhymes with Treasury," Carney joked in response to a reporter's question Thursday at a White House news briefing. "Because Treasury offers and gives licenses for travel, as you know and the White House has nothing to do with it."
Carney said the president did not communicate with Jay-Z over the trip.
"I am absolutely saying the White House, from the president on down, had nothing to do with anybody's personal -- anybody's travel to Cuba. That is something that Treasury handles."
The U.S. Treasury Department told Politico it gave approval for the trip's organizers to travel to Cuba as part of a cultural learning experience, but the department said it was not aware Jay-Z and Beyonce would be among the travelers.