Grayling, who is a close ally of Prime Minister Theresa May, told the Daily Mail on Friday that if MPs blocked Britain's departure from the EU, "we would see a different tone in our politics. A less tolerant society, a more nationalistic nation."
"'It will open the door to extremist populist political forces in this country of the kind we see in other countries in Europe," he said.
"If MPs who represent seats that voted 70 per cent to leave say 'sorry guys, we're still going to have freedom of movement,' they will turn against the political mainstream," he added.
Grayling's comments come after pro-Brexit protesters accused Conservative Remainer MP Anna Soubry of "being a Nazi" outside Parliament earlier this week.
Soubry has since called for the protester to be prosecuted by police.
One man who shouted the abuse told the BBC that his group would continue unless Britain left the EU on March 29, when Article 50 expires. Another was found to have argued last year that he wanted to "ban Islam from the west."
MPs are set to hold a "meaningful vote" on May's Brexit deal with the EU on January 15, which the government is likely to lose.
Labour and Rebel Tory MPs joined forces to back a key amendment to the Brexit process on Thursday, which meas the government will have to return with a fresh strategy for Brexit if the House of Commons rejects her deal.
