Everton banned The Sun tabloid from its premises on Saturday over an article about their player Ross Barkley that critics branded "racist".
The article in Britain's best-selling newspaper was about the 23-year-old England midfielder getting into a fight in a nightclub in Everton's home city of Liverpool.
Columnist Kelvin MacKenzie compared Barkley, who has a grandfather from Nigeria, to a "gorilla at the zoo" and said the only other people in Liverpool with his income were drug dealers.
The article was headlined "Here's why they go ape at Ross" alongside pictures of Barkley and a gorilla.
Everton said it had informed The Sun that the tabloid was banned from its Goodison Park stadium, its training ground "and all areas of the club's operation".
"Whilst we will not dignify any journalist with a response to appalling and indefensible allegations, the newspaper has to know that any attack on this city, either against a much-respected community or individual, is not acceptable."
Liverpool's mayor Joe Anderson said he had reported the article to the police and the Independent Press Standards Organisation, calling the comments "racist and offensive".
The Sun's publisher News UK said in a statement that MacKenzie "had been suspended with immediate effect".
"The paper was unaware of Ross Barkley's heritage and there was never any slur intended," the statement said.
It added the views expressed by MacKenzie about the people of Liverpool were "wrong, unfunny and are not the views of the paper".
MacKenzie said he had no idea of Barkley's family background and added: "For the mayor of Liverpool and a handful of others to describe the article as racist is beyond parody."
The Sun and MacKenzie are deeply unpopular in Liverpool. He was the paper's editor in 1989 when it published allegations about the behaviour of Liverpool Football Club fans in the Hillsborough stadium disaster.
Saturday marks the 28th anniversary of the tragedy in which 96 Liverpool supporters died.
Liverpool FC banned The Sun from their Anfield stadium and their training ground in February this year over the paper's 1989 Hillsborough coverage.
In his statement Friday, Anderson said there was a "sense of betrayal" that Everton had not done likewise.
If they did not do so before Saturday's English Premier League match against visitors Burnley, the mayor urged supporters to turn their backs to the pitch during the game.
Barkley was out celebrating his side's 4-2 win over champions Leicester City in the Premier League on Sunday when his lawyers said he was caught in an "unprovoked attack" in a nightclub.
In his column, MacKenzie wrote: "Perhaps unfairly, I have always judged Ross Barkley as one of our dimmest footballers.
"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.
"I get a similar feeling when seeing a gorilla at the zoo. The physique is magnificent but it's the eyes that tell the story.
"The reality is that at £60,000 ($75,000, 71,000 euros) a week and being both thick and single, he is an attractive catch in the Liverpool area, where the only men with similar pay packets are drug dealers."
The Sun said MacKenzie was on holiday and the matter would be investigated fully upon his return.