She told: "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The Conservative Party later confirmed she had had the whip withdrawn.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 prime minister and the Conservative Chief Whip, Gavin Williamson, were expected to meet to discuss the matter once Mrs May finished her Commons statement on last weekend's G20 summit earlier on Monday.
A Conservative spokesman said: "We are aware of these reports. This kind of language is completely unacceptable, and we are urgently investigating."
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 Conservative 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."
'Zero tolerance'
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 urged Mrs May to "act immediately" in response to what he said was "outrageous and completely unacceptable" language.
Green Party leader Caroline Lucas said there was "no place for racism, full stop" in British politics and Ms Morris should have the whip removed.
Ms Morris was also criticised by 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."
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.
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