A band spokesman said the show in the capital Havana on 25 March was “the first open air concert in Cuba by a British rock band”.
The Stones are currently on a Latin American tour due to end on 17 March in Mexico City.
The Havana gig will come three days after an historic visit to Cuba by US President Barack Obama.
In a statement, The Rolling Stones said: “We have performed in many special places during our long career, but this show in Havana is going to be a landmark event for us, and, we hope, for all our friends in Cuba too.”
The Stones’ America Latina Ole tour also includes shows in Brazil, Peru and Colombia.
The Havana gig will be filmed by director Paul Dugdale, who has previously worked with One Direction, Adele and Coldplay.