Terrence McNally's comedy is the first of play of the season to reach this financial landmark.
The recent Williamstown Theatre Festival production starred Chita Rivera and Roger Rees.
Both performers will step into their roles on January 7.
Nichols picked up eight Tony Awards for Best Director throughout his career.
The Tony-winning songwriters are set to receive the Oscar Hammerstein Award for Lifetime Achievement.
The Broadway revival celebrated its first night with Sarah Jessica Parker, Angela Lansbury, Louis C.K., Eddie Izzard, Kristin Chenoweth, Nick Offerman, and many more celebs.
The star-studded production also features Rupert Grint, Stockard Channing, Megan Mullally, and more.