The 24-year-old daughter of Cuban vice-president Marino Murillo defected earlier this month and is now living in Tampa, Florida, sources said.
Glenda Murillo Diaz crossed the Mexican border at Laredo, Texas, on around August 16, the sources said.
Her father is sometimes mentioned as a possible successor to Cuban President Raul Castro, who put Murillo in charge of enacting a series of profound economic reforms.
Murillo, 51, known as Cuba's "reforms tsar," is vice-president of the ruling Council of State and a member of the powerful political bureau of the Cuban Communist Party.
Glenda Murillo Diaz did not receive a US visa to visit relatives or study in the United States, said the sources, who asked to remain anonymous.
A person who claimed to have learned of Murillo Diaz's defection from her relatives in Havana had been sending anonymous tips to the Miami Herald since August 20, but the information could not be confirmed until Monday.
The young woman left Cuba about two weeks ago to attend a psychology conference in Mexico and turned up later at the Tampa home of a maternal aunt, Idania Diaz, who is married to Boris Loynaz, according to the source.
Her grandfather, Rolando Diaz, a Havana resident, happened to be visiting in Tampa when Murillo Diaz arrived, the person added. Her father broke down crying when he learned of the defection, another relative in Havana told several neighbours.
A young woman who identified herself only as Glenda Murillo started a Facebook page last Tuesday that described her as a 24-year-old psychology student at the University of Havana.
She posted one photo of herself somewhere hugging "Aunt Idy" and "Uncle Boris" and another smiling and leaning against an Elvis fortune-telling machine. The Elvis machine is at The Pier, a tourist attraction in St Petersburg, Florida.