"Phans" can use their artistic talents to win tickets to the long-running musical.
Annaleigh Ashford, Lisa Brescia, and more will perform in memory of the stage legend.
The environmentally minded season will also feature three international adaptations of Shakespeare's The Tempest.
A limited number of tickets will be available via lottery for performances from July 28-August 23.
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.