MacKenzie likened the England international to "a gorilla in the zoo"
The Sun columnist Kelvin MacKenzie has been suspended from the newspaper after he expressed "wrong" and "unfunny" views about the people of Liverpool, News UK has said.
Earlier, Merseyside Police said it was probing claims that a newspaper column about Everton star Ross Barkley amounts to a "racial hate crime".
The England international was punched twice in an "unprovoked" nightclub attack last weekend.
Writing about the incident, MacKenzie likened the England international, who has a grandfather born in Nigeria, to "a gorilla in the zoo".
He said that "thick and single" Barkley was "an attractive catch in the Liverpool area where the only men with similar pay packets are drug dealers".
He added: "There is something about the lack of reflection in his eyes which makes me certain not only are the lights not on, there is definitely nobody at home".
Liverpool mayor Joe Anderson said the remarks, which come a day before the 28th anniversary of the Hillsborough disaster, were "despicable" and a "racist slur" on Barkley.
MacKenzie was the editor of The Sun at the time of the 1989 tragedy and has since apologised for a front page story in which the tabloid claimed Liverpool supporters attacked police officers tending to injured fans and stole from dead bodies.
Anderson said he had reported MacKenzie and The Sun to the police and Independent Press Standards Organisation.
Addressing Everton FC, he tweeted: "Your lack of action in banning the S*n from your press conferences is a smack in the face to our city."
Merseyside Police told Sky News it had received a complaint "alleging that comments written about a third party constitute a racial hate crime".
It said: "Enquiries are now being carried out to establish the full circumstances of the incident.
"We take all allegations of hate crime extremely seriously and would encourage anyone who feels they have been the victim of a hate crime or who has witnessed one to contact us."
Memorial services have been held at Anfield most years since the Hillsborough disaster, but victims' families agreed that last year's service would be the final one.
From this year the city's two cathedrals will take it in turn to host simple commemorations.