Anne Marie Morris, the MP for Newton Abbot, used the phrase at an event in London to describe the prospect of the UK leaving the EU without a deal.
She told the BBC: "The comment was totally unintentional. I apologise unreservedly for any offence caused."
The Conservative Party later confirmed she had had the whip withdrawn.
Announcing the suspension, Theresa May said she was "shocked" by the "completely unacceptable" language.
"I immediately asked the chief whip to suspend the party whip," she said in a statement.
"Language like this has absolutely no place in politics or in today's society."
The BBC understands the prime minister and Conservative Chief Whip Gavin Williamson met to discuss the matter once Mrs May finished her Commons statement on last weekend's G20 summit.
According to a recording published on the Huffington Post website, Ms Morris was discussing the impact of Brexit on the UK's financial services industry at an event organised by the Politeia think tank, which was attended by other MPs.
Suggesting that just 7% of financial services would be affected by Brexit, she reportedly said: "Now I am sure there will be many people who will challenge that but my response and my request is look at the detail - it isn't all doom and gloom."
She went on: "Now we get to the real nigger in the woodpile, which is in two years what happens if there is no deal."
The phrase originated in the American Deep South in the mid-19th Century and is thought to have referred to slaves having to conceal themselves as they sought to flee north and secure their freedom.
It was subsequently used in the 20th Century - including by a number of leading novelists - as a metaphor to describe a hidden fact or problem.
The Lib Dems had called on Theresa May to withdraw the whip from Ms Morris, who was first elected to Parliament in 2010 and was subsequently re-elected in 2015 and earlier this year.
Leader Tim Farron said he was "shocked" and called for her to be suspended from the parliamentary party.
"This disgusting comment belongs in the era of the Jim Crow laws and has no place in our Parliament," he said.
Labour's Andrew Gwynne said Ms Morris had used "outrageous and completely unacceptable" language.
Green Party leader Caroline Lucas called on Ms Morris to resign as an MP, telling Sky News: "There is no place for her in the House of Commons."
She also claimed that other Conservative MPs at the meeting "apparently did not bat an eyelid" at Ms Morris's language.
"At the very least, there ought to be a conversation between Theresa May and the others in that room so that they're very clear going forward that if ever that kind of language is heard in the earshot, it has to be condemned immediately," Ms Lucas said.
Labour MP Chuka Umunna tweeted: "Speechless, not just at the remark being made but also at the reported lack of a reaction from the Tories there. Utterly appalling."
Politeia's website said MPs Sir William Cash, Kwasi Kwarteng and John Redwood also took part, though Mr Kwarteng told the BBC he was not there. The BBC has contacted the other MPs for comment.
Ms Morris did face criticism from Tory colleagues, one of whom, Heidi Allen, tweeted: "I'm afraid an apology is not good enough - we must show zero tolerance for racism. MPs must lead by example."
Fellow Conservative MP Helen Grant tweeted: "Inconceivable for an MP using that expression to be incognisant of its history, impact and complete unacceptability. So ashamed!"
In 2008, Conservative peer and party spokesman Lord Dixon-Smith apologised for using the same phrase in the House of Lords, saying that it was not appropriate and that he had "left his brains behind".
The peer was not dismissed.
A Conservative MP has been suspended from the party after it emerged she used a racist expression during a public discussion about Brexit.