The woman, Ginger White, told a local Atlanta television station that the on-and-off affair began in the mid 1990s. She said he flew her to different locations for secret meetings.
Miss White said they met after a business presentation by Mr Cain in the late 1990s and that for more than a decade he had flown her to cities around the United States where they had sex in upmarket hotels.
The single mother of two said that their physical relationship had ended eight months ago, shortly before he declared his presidential bid, but that they had spoken as recently as September.
“It was pretty simple,” White told the Fox Network station in Atlanta. “It wasn’t complicated. I was aware that he was married. And I was also aware I was involved in a very inappropriate situation, relationship.”
During an interview on CNN on Monday, the presidential candidate preemptively said he was expecting to face allegations of “an affair for an extended period of time” and denied any wrongdoing.
While Cain did not identify White by name during the appearance, he said of his accuser, “It is someone that I know who is an acquaintance that I thought was a friend. Here we go again,” Cain said on Monday. “I didn’t do anything wrong.”
Republican strategist Ed Rollins said the latest allegation could be fatal to the former Godfather’s Pizza CEO’s presidential ambitions. “I think it’s the final nail in the coffin,’ he said. “I think he was going down pretty fast anyway.”
“With five weeks to go before voters start participating, it’s not a good place to start reinvigorating your campaign,” he said, referring to early Republican electoral contests which begin in January in Iowa.
Mr Cain admitted he knew Miss White from his native Georgia but said she only had his phone number because he was trying to help her find a job and that claims of an affair were “completely baseless”.
“Detractors are trying once again to derail the Cain Train with more accusations of past events that never happened.
“The Cain Campaign is not surprised that another female accuser has come forward due to the fact that earlier allegations were unable to force Herman Cain to drop his presidential bid to renew America,” his campaign said in a statement.
Cain in a CNN interview called White a “friend,” and said he had nothing to hide and that he is staying in the race.
But asked if he would drop out of the campaign due to the stream of allegations, Cain said: “I would make that decision depending on the circumstances and how it is impacting my wife and my family.”
“I’m not dropping out of this race, no. As long as my wife is behind me,” he said.
Miss White’s claims come weeks after it was revealed that two women had been paid compensation by the National Restaurant Association after they complained Mr Cain had sexually harassed them while he was CEO of the organisation.
One woman was paid $45,000 (£29,000), while the other received $35,000 (£25,500). White’s mobile phone bills showed she had contact with him 61 times in recent months, often receiving calls or texts in the early hours of the morning.
“He made it very intriguing. It was fun. It was something that took me away from my humdrum life at the time,” she told Fox Atlanta.
Mr Cain has denied all the accusations but they have nonetheless caused major damage to his bid to become the Republican candidate to take on President Barack Obama in next year’s election.
For several weeks he led in the polls but has since fallen to third place behind former Speaker of the House Newt Gingrich and former Massachusetts governor Mitt Romney. [via Reuters and Huffington Post]