The show, which opened in 1960, was awarded Tony Honors for Excellence in Theatre in 1991.
Based on the Nicholas Sparks' novel, the musical starts previews next year.
The feminist update on fairytales features the music of a real-life pop princess.
Harnick and composer Jerry Bock made up the premier musical-theater songwriting duos of the 1950s and 1960.
New dates have been added and are already selling fast.
The show will also feature special performances to honor Joel Grey and John Kander, recipients of special Tony awards for lifetime achievement in the theatre.
"The hazardous air quality in New York City has made it impossible for a number of our artists to perform this evening," reads a statement from "Hamilton's" producers.
This pre-show leads directly into the Tony Awards, hosted by Ariana DeBose.
Two other musicals, Shucked and a Sweeney Todd revival, also win multiple awards.
The musical film also features Ciara, Danielle Brooks and Taraji P. Henson.
