"The alleged row centred on a parody of Fox News' rolling news ticker, which included headlines such as "Do Democrats cause cancer?"
Mr Groening said the news channel backed down because it would have caused Fox to bring a lawsuit against itself.
"Fox said they would sue the show and we called their bluff because we didn't think Rupert Murdoch would pay for Fox to sue itself. We got away with it," Mr Groening told National Public Radio in the US.
"But now Fox has a new rule that we can't do those little fake news crawls [tickers] on the bottom of the screen in a cartoon because it might confuse the viewers into thinking it's real news," he added on NPR's Fresh Air programme."