Without elaborating, the US president-elect tweeted that the newspaper had changed the terms of the meeting.
He posted: “They continue to cover me inaccurately and with a nasty tone!”
Mr Trump has had an antagonistic relationship with the press, railing against liberal bias, even while benefiting from blanket TV coverage.
I cancelled today's meeting with the failing @nytimes when the terms and conditions of the meeting were changed at the last moment. Not nice
— Donald J. Trump (@realDonaldTrump) November 22, 2016
Early on Tuesday, he tweeted that he had called off his meeting with what he always refers to as the “failing” New York Times.
The Republican – known to be an avid consumer of newspapers and news shows – said the newspaper had switched the terms at the last moment, adding: “Not nice.”
But Jonathan Mahler, a political correspondent for the New York Times, tweeted that it was Mr Trump who had tried to change the rules of engagement.
He said the Republican had asked for the discussion to be private and off-the-record, but the daily had refused.
The newspaper said it had been unaware the meeting was cancelled until Mr Trump tweeted.
On Monday evening, he invited leading figures from the American TV networks for an off-the-record briefing at Trump Tower, where they were subjected to a tirade about election reporting.
The media executives and anchors – including NBC’s Lester Holt, CNN’s Wolf Blitzer and ABC’s George Stephanopoulos – were apparently expecting to discuss coverage of his presidency.
But instead Mr Trump reportedly labelled them “liars” and called journalists the “lowest form of humanity”.
One attendee leaked the details to the New York Post, saying: “The meeting was a total disaster.
“The TV execs and anchors went in there thinking they would be discussing the access they would get to the Trump administration, but instead they got a Trump-style dressing down.”
The New York Times reports that during his complaint about “dishonest” coverage Mr Trump singled out CNN president Jeffrey Zucker.
According to the Washington Post, Mr Trump also referred to NBC’s Katy Tur and ABC’s Martha Raddatz, without naming them.
Throughout his campaign Mr Trump accused the media of dishonesty, sometimes targeting individual journalists at his rallies and even denying some outlets accreditation to his events.
He feuded with Fox News anchor Megyn Kelly, who later alleged that he had offered her gifts, including hotel stays, in an attempt to influence coverage.
The presenter said she was not the only journalist who had been offered freebies by Mr Trump.
Two weeks after his shock election victory, Mr Trump has yet to hold a news conference, and US media outlets have griped that no president-elect has delayed holding a press briefing for so long since Jimmy Carter in 1976.