The debate -- being organized in partnership with the Republican Party -- would have been held Monday in Salt Lake City, Utah.
"The Salt Lake City debate is canceled," said a statement from Fox News' executive vice president of news, Michael Clemente.
"I think we've had enough debates," Trump had told the same network earlier.
Already on Friday, the billionaire had told reporters he thought it was time to end the debates.
Twelve Republican debates have been held since August. Trump already boycotted one such forum held in Iowa in late January, also hosted by Fox News.
Instead of taking to the stage in Utah, Trump said he would be delivering a speech in Washington at an annual conference held by AIPAC, a pro-Israel lobbying group. Top Democratic White House contender Hillary Clinton is also due to speak at the gathering.
Ohio Governor John Kasich had let it be known that he probably wouldn't participate in the debate either in the absence of Trump.
"We had hoped to contrast Governor Kasich's positive, inclusive approach to problem solving with Trump's campaign of division. If he changes his mind, we will be there."
Remaining rival Ted Cruz has also decided to back out of the debate, according to broadcaster CBS.
"Ted Cruz has expressed a willingness to debate Trump or Kasich -- or both. But obviously, there needs to be more than one participant," Clemente said.
In 2007 and 2008, Barack Obama and Clinton also faced off more than 20 times.
