Robert Cuccioli, Melissa O'Neill, and Jesse Manocherian will star.
The musical show features music and lyrics by Bridget Everett, Marc Shaiman, and Scott Wittman.
The Hitchcockian drama opened October 2.
The theater company responds to the financial realities of writers.
The musical favorites will touch down at the Palace Theatre.
The musical, featuring a score by Motown legends Holland-Dozier-Holland, will play Chicago's Oriental Theatre.
Barron's plays include You Got Older and Baby Screams Miracle.
The performance is adapted for children with autism spectrum disorders and other sensory sensitivities.
The event gets kids into shows for free when accompanied by a full-paying adult.
The seventh concert of the Broadway Sings concert series will also feature Christine Dwyer and Zak Resnick.