In an "Entertainment Tonight" interview that aired Tuesday, Dickinson said that the 1982 incident occurred in Lake Tahoe, California, where he was appearing.
She told the TV newsmagazine that she wrote about the assault in her 2002 autobiography, No Lifeguard on Duty: The Accidental Life of the World's First Supermodel, but that Cosby and his lawyers pressured her and the publisher to remove the details.
A call to Cosby's publicist seeking comment was not immediately returned.
In the interview, Dickinson said she met Cosby in Lake Tahoe at his urging after he said that he would help her with her singing career. They had met earlier when her agent had introduced them, hoping that she could get a job on "The Cosby Show."
Dickinson said that after dinner, she and Cosby were in her hotel room and that he gave her some red wine and a pill. She told "Entertainment Tonight" she had asked for a pill because she had been suffering stomach pains.
"The next morning I woke up and I wasn't wearing my pajamas and I remembered before I passed out I had been sexually assaulted by this man," she said. She said she remembered Cosby dropping the robe he had been wearing and getting on top of her.
She said she never confronted Cosby about the incident.
"I'm doing this because it's the right thing to do and this happened to me and this is a true story," she said.
In the memoir, Dickinson described stopping herself at his hotel room door when he invited her in after dinner, claiming exhaustion.
"After all I've done for you, that's what I get? 'I'm exhausted,'" Dickinson quoted Cosby as saying. He then "gave me the dirtiest, meanest look in the world, stepped into his suite, and slammed the door in my face," she wrote.
Cosby (77) who was never criminally charged in any case, settled a civil suit in 2006 with another woman over an alleged incident two years before.
Attention to the legendary entertainer's past flared suddenly in recent weeks after another comic, Hannibal Buress, called Cosby a "rapist" during a Philadelphia performance. Two other women have emerged as accusers, including Barbara Bowman, who wrote an online Washington Post piece.
Cosby has remained silent, and his attorney, John P. Schmitt, issued a statement Sunday saying his client would not dignify "decade-old, discredited" claims of sexual abuse with a response. Schmitt later exempted the 2006 civil case from the blanket statement.