The writer, Blake Neff, this week allegedly responded to a racist question posed by another user which asked if people would let a “JET BLACK congo n*****” perform Lasik eye surgery on them.
“I wouldn’t get LASIK from an Asian for free, so no,” Mr Neff responded, according to CNN, which first reported the allegations.
Fox News told The Independent Mr Neff had resigned, and Carlson has been approached for comment.
Mr Neff, who worked at Fox News for four years, had previously been praised by Carlson, who in 2018 called his colleague a “wonderful writer” and in a book acknowledged Mr Neff for helping with research.
In an interview published recently by Dartmouth Alumni Magazine, Mr Neff said: “Anything [Carlson] is reading off the teleprompter, the first draft was written by me.”
Carlson himself has been repeatedly accused of making racist remarks on-air, and was earlier this week hailed as a potential replacement for Mike Pence as Donald Trump’s 2020 running mate by former KKK leader David Duke.
In other alleged racist comments made on online platform AutoAdmit, Mr Neff reportedly wrote that black men “playing Call of Duty is probably one of the biggest factors keeping crime down”, and said that Democrat politicians including Alexandria Ocasio-Cortez wanted to make the US “a dumping ground for people from third world s***holes".
It is also claimed he mocked women online, including comments over a five-year period about one woman he was Facebook friends with.
Mr Neff could not be reached for comment, but in a memo emailed to staffers, Fox News said Mr Neff had made "horrendous and deeply offensive racist, sexist and homophobic comments" on the online forum.
"We want to make abundantly clear that Fox News Media strongly condemns this horrific racist, misogynistic and homophobic behaviour. Neff's abhorrent conduct on this forum was never divulged to the show or the network until Friday, at which point we swiftly accepted his resignation," the memo read.
"Make no mistake, actions such as his cannot and will not be tolerated at any time in any part of our workforce."
Carlson, a close confidant of Donald Trump, has recently lost lucrative deals with major advertisers after he said that the “Black Lives Matter” movement “certainly isn’t about Black lives, and remember that when they come for you. And at this rate, they will”.
He has also previously said that allowing “the world’s poor” into the US will make it “poorer and dirtier”, bemoaned Somalian congresswoman Ilhan Omar as “living proof that the way we practice immigration has become dangerous to this country”, and dismissed white supremacy as “not a real problem” just after a self-professed racist shooter killed 22 people in El Paso, Texas.