To be directed by John Crowley, the production will mark the play's world premiere. It will also be the British playwright's first play to originate on Broadway.
Previews are to begin Feb. 18 and it is to open March 4 at New York's Gerald Schoenfeld Theatre for a 16-week run.
"The title is just the starting point; take a man searching for his missing hand, two con artists out to make a few hundred bucks, and an overly curious hotel clerk, and the rest is up for grabs," the show's producers said in a release.
They said the black comedy will be McDonagh's first American-set play.
McDonagh's other works include the stage dramas "The Beauty Queen of Leenane," "The Lonesome West," "The Pillowman" and "The Lieutenant of Inishmore." He wrote and directed the movie "In Bruges," as well.
Walken's New York theater credits include performances in "The Lion in Winter," "The Seagull," "The Rose Tattoo" and "James Joyce's The Dead."