The production is set to run at Madison Square Garden.
Craig "muMs" Grant and Melissa Ross will also have their works presented.
Aaron Mark will direct the new solo show.
Martin takes on the role of Berthe, for which she won a 2013 Tony.
The cast will also include Christopher Fitzgerald, Isaiah Johnson, and David Turner.
The 54 Below event will feature performances and anecdotes from "everyone's favorite newsboys (and girls)."
The historical musical features a Tony-winning book and score by Alfred Uhry and Jason Robert Brown.
The acclaimed composers will present concerts and classes as part of WPPAC's Creating Broadway Series.
MCC Theater will present the world premiere of LaBute's latest comedy this fall.