Virginia, who is now married and has the surname Giuffre, says in the clip: "It was a really scary time in my life.
"[Prince Andrew] knows what happened, I know what happened. And there's only one of us telling the truth."
The Panorama special will be aired in the UK on Monday, December 2.
Virginia has claimed in court papers in Florida that she was forced to have sex with Andrew when she was aged 17, which is below the state's age of consent.
Her allegations, which Andrew strenuously denies, were struck from US civil court records in 2015 after a judge said they were "immaterial and impertinent".
Her televised interview follows Andrew's attempt to defend himself against these accusations and explain his friendship with Jeffrey Epstein during an interview on BBC's Newsnight which was branded a "car crash".
Prince Andrew has stepped down from royal duties following his interview.
Andrew's interview featured a number of eyebrow-raising admissions, but none more so than his excuse to his whereabouts on the day that Virginia Roberts claimed that Epstein trafficked her for sex with him in London.
The Duke of York claimed he could not have had sex with a teenage girl in the London home of his "good friend" British socialite Ghislaine because he was at home after attending a children’s party at Pizza Express in Woking, England.
Andrew, dad to Beatrice, 31, and Eugenie, 29, with ex-wife Sarah Ferguson, said: “That couldn’t have happened because the date being suggested — the 10th of March — I was at home with the children.
“I’d taken Beatrice to a Pizza Express in Woking for a party at about 4 or 5 in the afternoon and then because the Duchess was away, we have a simple rule in the family that when one is away the other is there.”
He was asked why he could remember going for something so mundane as a pizza 18 years on, and he added: "Because going to Pizza Express in Woking is a very unusual thing for me to do. I’ve never been . . . I’ve only been to Woking a couple of times and I remember it weirdly distinctly. As soon as somebody reminded me of it, I went, 'Oh yes I remember that.'"