He had been making an announcement to the performers in this year's festival at Wexford's Theatre Royal when he collapsed.
Hynes was appointed managing director of the Wexford festival in 1998, and later was appointed chief executive. His background includes managing the Druid Theatre Company in Galway.
He was appointed deputy chair of the Irish Arts Council in 2003, and also chaired a special committee on the traditional arts.
The 54-year-old Wexford Festival, located on the southeastern coast of Ireland, is known for its performances of operatic rarities. It runs from October 20 to November 6 this year.