Johansson will play Maggie the Cat in her performance on Broadway since she won a Tony in the Arthur Miller play 'A View from a Bridge' in 2010.
"I am so thrilled to return to Broadway and feel incredibly fortunate to be doing so with Rob Ashford and such gifted actors."
Benjamin Walker of 'Bloody Bloody Andrew Jackson' will star as Maggie's alcoholic ex-athlete husband, Brick.
Ciaran Hinds of 'Game of Thrones' will play Brick's blustery plantation-owner father, Big Daddy. Tony winner Debra Monk will play Big Mama. The show is being produced by Stuart Thompson, The New York Times reported.
The play will begin preview performances at the Richard Rodgers Theater on December 18 and open on January 17, 2013.
Williams' play is a classic about the disintegration of a wealthy Southern family. It was revived on Broadway just four and a half years ago in an all-black production, and before that during the 2003-4 theater season.
Elizabeth Taylor has already immortalised Maggie in a big screen adaptation of 'Cat on a Hot Tin Roof' 1958 film.