Mr Fox, who is an outspoken critic of Mr Trump, lampooned the president for asserting which groups were welcome in America and said his mouth was the “foulest sh*thole in the world”.
“Donald Trump, your mouth is the foulest sh*thole in the world. With what authority do you proclaim who’s welcome in America and who’s not," he said on Twitter.
Mr Fox then went on to question whether Mr Trump, whose family originally comes from Germany, had forgotten his own immigrant heritage. The president's mother was born in Scotland came to America at the age of 17.
The businessman, who was president of Mexico from 2000 to 2006, said: “America’s greatness is built on diversity, or have you forgotten your immigrant background, Donald?”
This comes after Mr Trump reportedly branded Haiti and several African countries “sh*thole” nations during a meeting with congressional leaders in the Oval Office.
After ideas for restoration projects to help immigrants in Haiti, El Salvador, and African countries were floated as a potential part of a bipartisan immigration deal, the world leader is said to have become frustrated.
"Why are we having all these people from s***hole countries come here?" Mr Trump asked, two people briefed on the meeting told the Washington Post.
Mr Trump then reportedly suggested the US should instead bring more people from countries like Norway, a nation whose prime minister met with the president on Wednesday.
The White House did not deny Mr Trump's reported comments in a statement to reporters. When asked to comment on the story White House spokesman Raj Shah said: “Certain Washington politicians choose to fight for foreign countries, but President Trump will always fight for the American people".
This is the most recent example of Mr Trump referring to Haitians in a problematic manner. According to earlier reports, the world leader voiced contempt for immigrants from Haiti and claimed all of the people coming to the US from the island have “Aids”.
Mr Fox, who has regularly criticised Mr Trump on Twitter over his stance on immigration, contests the president’s plan for a wall or fencing on the US Mexico border and disagrees with Mr Trump's proclamation Mexico will pay for it.
"You can use my words. We will never pay for that f****** wall," he said in a strongly worded statement over the summer.
He continued: "Who can think about a country paying for a wall that is going to be built in the neighbour's territory? Or why should Mexico pay for a wall? What's the reason? We don't need a wall."
Mr Fox mocked Mr Trump for his golfing trip over the summer, quipping he should simply leave the White House if he is unhappy with his role there.
“[L]eaving on vacation, huh? What for? If you're not happy with your job, just leave. After all, it was never for you,” he tweeted.