The Lerner and Loewe musical with Broadway plans will play the Kennedy Center
Michael McElroy, Jennifer Leigh Warren, and others will also participate.
The theater was last home to the musicals Mamma Mia! and Rocky.
The play will feature a rotating cast including Brian Dennehy, Mia Farrow, Carol Burnett, and more.
Brooks is celebrating the 40th anniversary of his film Young Frankenstein, which was adapted for the Broadway stage in 2007.
The Armory will host two new productions from Trusty Sidekick Theater Company.
The rare revival production adds performances to its limited run.
The evening will take place before the release of the new film adaptation of the musical.
A.R. Gurney's drama tells the story of 10 people at a roadside motel.
The three-part epic by Pulitzer Prize winner Suzan-Lori Parks comes to the Public this fall.