Sharon Bialek, who worked at the restaurant group's eduction foundation until shortly before the alleged groping incident, said Cain unexpectedly put his hand beneath her skirt and between her legs "toward my genitals." She also said he pushed her head toward his crotch.
Cain stopped when she protested, Bialek told a news conference.
Looking into the television cameras, Bialek said: "I want you, Mr. Cain, to come clean. Just admit what you did."
The accusation follows the disclosure last week that the restaurant association provided payments to two women who left the group after alleging sexual harassment by Cain, also in the late 1990s.
Cain has denied all accusations of sexual harassment, and his campaign put out a fresh denial after Bialek made her accusations on Monday.
"All allegations of harassment against Mr. Cain are completely false," a campaign statement said. "Mr. Cain has never harassed anyone."
Since becoming public on October 30 in a report by Politico, the sexual harassment accusations have overwhelmed the bid by the former pizza company executive to win the Republican presidential nomination.
Cain, a favorite of tea party conservatives, has risen to the top of the polls following strong performances in several debates and the release of his "9-9-9" tax plan that sets flat 9% rates for corporate and income taxes and also creates a 9% national sales tax.
However, Bialek's accusation raises fresh questions about whether Cain has been candid about the allegations that he sexually harassed women at the restaurant association when he headed the group from 1996-99.
Bialek said she started to work at the group's foundation in 1996 but was laid off in 1997. Shortly thereafter, she contacted Cain -- whom she had met at the group's Chicago convention -- to seek help in finding a job.
She traveled to Washington, where Cain worked, and found he had upgraded her hotel room to a luxury suite without telling her. They had dinner at an Italian restaurant, she said, and then Cain asked if she had been to the association offices in the capital.
Cain made his advances as on the way, according to Bialek.
"He said, 'You want a job, right?' " she told reporters at the news conference organized by celebrity attorney Gloria Allred.
Bialek took no questions from reporters, but Allred said Bialek had told two people at the time about what happened. Bialek filed no complaint with the restaurant association because she no longer worked there, Allred said.
Asked why Bialek was coming forward now, Allred said it was in solidarity with Cain's other accusers and harassed women everywhere.
Cain has previously complained the sexual harassment allegations amount to a baseless media onslaught against his campaign.
On Saturday, Cain scolded reporters who asked about the issue following a debate with fellow conservative Newt Gingrich in Texas.
"Don't even go there," Cain told one questioner who'd asked about the allegations. Asked again later, he responded: "What I'm saying is this -- we are getting back on message, end of story. Back on message. Read all of the other accounts, where everything has been answered -- end of story."