Tickets for When We Have Sufficiently Tortured Each Other will not fo on general sale, with the theatre electing to operate a balloting system for the play's six-week run, which begins in January.
The Australian-born, Academy Award-winning actress will appear in alongside Game Of Thrones actor Stephen Dillane, who returns to the National Theatre for the first time since The Coast Of Utopia in 2002.
According to the National Theatre, the play "breaks through the surface of contemporary debate to explore the messy, often violent nature of desire and the fluid, complicated roles that men and women play".
The production is based on Samuel Richardson's 1740 novel Pamela and sees "six characters act out a dangerous game of sexual domination and resistance".
Blanchett has an extensive career on stage as well as starring in films including Notes On A Scandal, Blue Jasmine and Ocean's 8.
The ballot opens at midday on Thursday, 22 November and runs until midday on Thursday November 29.
Tickets for the show, staged at the National's Dorfman Theatre from January 16 to March 2 next year, are expected to cost from between £10 to £58.
Additional reporting by agencies.
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