Anne Marie Morris, who represents Newton Abbot in Devon, is under investigation over the comment she made at an event attended by Brexit-backing MPs.
In an audio clip recorded by the Huffington Post website, she is heard using the phrase “the real n***** in the woodpile”.
Ms Morris, who was first elected to Parliament at the 2010 general election, described her comment as “entirely unintentional”, adding: “I apologise unreservedly for any offence caused.”
She was speaking at an event on Monday to discuss Britain’s future financial services relationship with the EU, hosted by the Politeia think tank at central London’s exclusive East India Club.
Prime Minister Theresa May said: “I was shocked to hear of these remarks, which are completely unacceptable.
“I immediately asked the chief whip to suspend the party whip. Language like this has absolutely no place in politics or in today’s society.”
The suspension of Ms Morris could add further pressure on Mrs May’s minority Government during forthcoming votes in the House of Commons, following the Prime Minister’s disastrous General Election result.
The Tories have been left relying on the DUP for support in order to pull together a fragile majority of MPs.
Ms Morris’s remark is reported to have been made in reference to Britain potentially leaving the EU without a Brexit deal, with Ms Morris recorded saying: “And then we get to the real n***** in the woodpile which is in two years what happens if there is no deal?”
Fellow Brexit-supporting MPs Sir Bill Cash and Sir John Redwood were also scheduled to speak at the event.
A spokesperson for Politeia said: “The MP has apologised unreservedly and we are happy she has apologised.”
Rival politicians demanded the Tories cut ties with Ms Morris over her remark, who was also told to consider resigning as an MP.
Green Party co-leader Caroline Lucas told Sky News the “right thing” for the Conservative backbencher to do would be for her to quit Parliament.
Ms Lucas said: “I’m very glad that Theresa May has taken this action, it has taken her a number of hours to do so and I think it might have been more reassuring had she spoken out more quickly.
“And I think she also needs to address the fact there were other Conservative MPs there in the room at the time who apparently didn’t bat an eyelid about this either.
“The bottom line is this kind of language, these kind of attitudes, have absolutely no place in modern Britain.”
She added: “A lot of people will have taken very, very serious offence at the words that she spoke.”
Outgoing Liberal Democrat leader Tim Farron said: “The Conservative Party should withdraw the whip from Anne Marie Morris and they should do it today.
“Every hour they leave her in place, is a stain on them and the so called ‘compassionate conservatism’ they supposedly espouse.
“I am utterly shocked that this person represents the good people of Newton Abbot.”
Andrew Gwynne MP, Labour’s co-national campaign co-ordinator, branded Ms Morris’s comments “outrageous and totally unacceptable”.
He said: “Theresa May once spoke about changing the Tories’ ‘Nasty Party’ tag. If she’s serious about that, she will admit it’s not enough for the Tories to ‘investigate’ and will apologise and act immediately.
“If that means withdrawing the whip, that’s what they should do.”
In 2008, then-Conservative leader David Cameron stood by Lord Dixon-Smith after the Tory peer apologised for using the same phrase as Ms Morris during a debate in the House of Lords.
The dated figure of speech was common in the late 19th and early 20th centuries, when it was frequently used in literature and film.
In 2007, former Tory MP Patrick Mercer was forced to resign from his party’s front bench after making comments about race in the Army, which Mr Cameron described as “completely unacceptable”.