Ginger White, a Georgia businesswoman, told an Atlanta television station on Monday that the affair lasted for 13 years.
"It wasn't complicated. I was aware that he was married," said White. "And I was also aware I was involved in a very inappropriate situation, relationship."
Cain acknowledged that he knew White but has denied the extramarital affair.
"I did not have an affair," said Cain. "And until I see and hear exactly what's going to be, what accusations are going to be made, let's move on."
This recent accusation follows a string a sexual harassment allegations against the GOP candidate.
Several women have come forward claiming Cain sexually harassed or groped them while he was a high-ranking official at the National Restaurant Association more than a decade ago.
He has denied any wrongdoing, although his rise in opinion polls has been reversed in the days since the accusations came to light.
The Associated Press contributed to this story.