The comedy-drama, adapted from the 2009 Tony Award-winning play God of Carnage, will open the festival on September 30.
Carnage boasts a cast including Inglourious Basterds star Christoph Waltz, Academy Award winners Kate Winslet and Jodie Foster and Chicago actor John C. Reilly.
The film follows two couples from Brooklyn who meet up one evening to discuss a playground fight that their children had.
"From Knife in the Water to Repulsion to The Tenant, Roman Polanski has shown himself to be an absolute master at making the most restricted spaces come to dramatic life," selection committee chair Richard Peña told The Hollywood Reporter.
"In Carnage, aided by four remarkable performances, he has reached a new pinnacle in his already extraordinary career."
Carnage has been included in the selection for this year's Venice Film Festival, alongside films from George Clooney, Madonna and David Cronenberg.
The New York Film Festival runs through to October 16.