A spokesman for the cinema chain due to host the screening said it had been shelved.
Hackers targeting Sony Pictures had threatened to attack US cinemas showing the studio’s film.
They belong to the same group which has released emails and data stolen from Sony.
Calling themselves Guardians of Peace, the hackers mentioned the 9/11 attacks in a recent warning, claiming “the world will be full of fear”.
“Remember the 11th of September 2001. We recommend you to keep yourself distant from the places at that time,” the hacker group wrote in a message on Tuesday.
“If your house is nearby, you’d better leave,” they add. “Whatever comes in the coming days is called by the greed of Sony Pictures Entertainment.”
The Department of Homeland Security said there was “no credible intelligence to indicate an active plot” against cinemas, but noted it was still analysing messages from the group.
A spokesman for Landmark, the cinema chain due to host the New York premiere, confirmed the showing had been cancelled but gave no reason, Reuters news agency reported.
Executives from Sony had previously said they would not object if cinemas chose not to show The Interview.
Carmike Cinemas, which operates 278 venues across the country, has cancelled planned screenings, according to several news outlets.
Others have backed the movie. “If they play it, we’ll show it,” said Tom Stephenson, CEO of Look Cinemas.
“Sony has a right to make the movie, we have a right to play it and censorship in general is a bad thing.”
The film’s stars, James Franco and Seth Rogen, have also pulled out of several media appearances including appearances on the chat shows Late Night with Seth Meyers and The Tonight Show Starring Jimmy Fallon.
Guardians of Peace have also released a new trove of Sony company data, calling it a “Christmas gift”.
A cache of company emails, social security numbers and salary details had already been released.
On Tuesday, two former Sony Pictures employees sued the California company for not providing adequate security to prevent the computer breach.
The studio earlier attempted to limit the damage by contacting some US news outlets to block the publication of the emails.
Some of the emails released have contained embarrassing exchanges about some of Hollywood’s biggest stars, among them Angelina Jolie and Leonardo DiCaprio.
Variety, the New York Times and the Hollywood Reporter were informed the studio “does not consent to your possession… dissemination, publication… or making any use of the stolen information”.
North Korea has denied involvement in the attack, but has described it as a “righteous deed” that may have been carried out by its “supporters and sympathisers”.
According to Variety’s Andrew Wallenstein, however, publishing the stolen data is “problematic but necessary” because it “is in the public domain” and “unavoidable”.