Born John Keyes Byrne in Dalkey, the writer is best known for his play "Da," which was adapted into a film starring Martin Sheen and the late Barnard Hughes, as well as for his "Curmudgeon" column that ran in Ireland's Sunday Independent newspaper.
Leonard's other plays include "The Big Birthday," "A Leap in the Dark," "Stephen D.," "The Poker Session," "The Patrick Pearse Motel" and "The Au Pair Man."
The BBC said Leonard had been undergoing treatment for an undisclosed illness at a Dublin hospital when he died.
"Hugh will be greatly missed by all who had the pleasure of his company and counsel throughout the years," the BBC quoted Irish President Mary McAleese as saying. "(He) infused his work with a unique wit, all the while demonstrating a great intuition, perceptiveness and forgiveness of human nature."
Irish Prime Minister Brian Cowen said, "Hugh will be remembered as a great literary figure of modern Ireland."