Republican National Committee (RNC) Chairman Reince Preibus said CNBC's moderators subjected the candidates to unfair, "mean-spirited" questions.
NBC called the RNC's decision to end their agreement to broadcast the 26 February debate "disappointing".
The RNC said the debate would still be held, but would not air on NBC.
The group did not specify whether another network would broadcast the debate.
"Candidates were promised that speaking time would be carefully monitored to ensure fairness. That was not the case," Mr Preibus wrote in a letter.  "Questions were inaccurate or downright offensive."
The Republican National Committee has been sharply criticised by some campaigns for its handling of the debates, so this move could be seen as an attempt to deflect blame onto that traditional conservative punching bag, the media.
In reality, the questions from CNBC moderators - while occasionally inelegant - were not too different in tone or content than those of earlier gatherings.
The move comes ahead of a reported meeting in Washington on Sunday by representatives from a number of the campaigns where they plan to discuss significant changes to the debate format and process - without RNC input.
A rebellion against the RNC over the debates has been brewing for some time, and severing ties with NBC could be an attempt to ease those tensions. At this point, however, it may not be enough.
During the debate, moderators questioned the figures behind some candidates' tax plans, causing several to have heated exchanges with journalists Becky Quick and John Harwood.
CNBC is NBC's business news network so many of the questions focused on economic policy and the previous work experience of CEO candidates Donald Trump and Carly Fiorina.
"The questions that have been asked so far in this debate illustrate why the American people don't trust the media," Texas Senator Ted Cruz, one of the candidates, said during the debate. "This is not a cage match."
Mr Cruz said the moderators insinuated that Mr Trump was "a comic-book villain" and retired neurosurgeon Ben Carson "was bad at math".
Some US journalists have defended the line of questioning and political fact checkers found the candidates frequently misrepresented facts.
NBC said that it would continue to work with the RNC to address its concerns, holding out hope the debate could still be broadcast by the television network.
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A coming US presidential debate will not air on NBC after Republicans said this week's forum on a sister network was conducted in "bad faith".