The trip will be the first for the jazz band. The ensemble will perform several concerts from Oct. 5 to 9.
Later in the month Jazz at Lincoln Center will produce the Afro-Cuban Jazz Celebration, featuring concerts in New York City.
Marsalis says he "can't wait" for the chance to play in Cuba.
Travel by Americans to Cuba is restricted. The trip was approved by U.S. authorities.
Funding for the visit was provided by the Andrew W. Mellon Foundation, the Ford Foundation, the Rockefeller Foundation and two smaller foundations.