Anne Marie Morris, who represents Newton Abbott, described the UK leaving the EU without a deal as a “real n*****r in the woodpile” at a meeting of eurosceptics in London, the Huffington Post reported.
Tory MPs Bill Cash and John Redwood, who were also on the panel with Morris, did not react when she said the remark.
MPs have called on the Tories to cut the party’s ties with Ms Morris.
Outgoing Liberal Democrat leader Tim Farron said: “This disgusting comment belongs in the era of the Jim Crow laws and has no place in our Parliament.
“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.
“Even if she misspoke this is the nastiest thing I’ve heard an MP utter since Lord Dixon Smith uttered the same awful phrase a few years ago.”
Green Party co-leader Caroline Lucas tweeted: “Appalling. Should have the whip removed immediately.
“No place in our politics for racism, full stop.”
Morris later said her comment was “entirely unintentional”, adding: “I apologise unreservedly for any offence caused”.
Last month, Morris was forced to distance herself from comments made by her electoral agent and partner who claimed ‘that the crisis in education was due entirely to non-British born immigrants and their high birth rates’.
A Conservative spokesman said: “We are aware of these reports, this kind of language is completely unacceptable, and we are urgently investigating”