Daryl Roth will produce the reading, which is scheduled for Oct. 18 at the Broadway venue. The reading will raise funds for both the Actors Fund and Friends in Deed.
Casting has yet to be announced.
Director Grey starred in the original production of The Normal Heart at The Public Theater, in which he played the central role of Ned, based semi-autobiographically on playwright Kramer. (Grey succeeded Brad Davis, who originated the role.) The Normal Heart focuses on "the terrifying early years of the AIDS epidemic in New York and the criminal silence of official America in dealing with it."