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 .
“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.”
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 US, has cancelled planned screenings, according to several news outlets.
The company has not yet commented publicly on the reports.
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 December 16, 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 news outlets to block the publication of the emails.
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 sympathizers”.
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