The free reading, which will also star Tony nominee Kate Burton, will be broadcast live on BBC Radio Wales.
The Poetry Center presented the premiere of the play, with Thomas himself leading the cast, in May 1953.
Sheen said in a statement, "It's a real honor and an absolute thrill to be able to perform Under Milk Wood in this very special year and on the stage that it first found its voice. The live radio broadcast is an opportunity to celebrate him and his work in both New York—a city that became so important to Dylan—and, at the same time, in Wales, his inspiration and home.”
"Dylan Thomas in America," an exhibition of photos, letters, drawings and manuscripts that chronicles the poet’s trips to the U.S. in the 1950s, will also be available for viewing in the 92Y’s Weill Art Gallery.