In the 20-second clip, Giuffre, formerly Virginia Roberts, said: “He knows what happened, I know what happened and there’s only one of us telling the truth”.
Giuffre has previously claimed she was trafficked to the UK to meet the duke in 2001 by sex offender Jeffrey Epstein. In the clip she describes the period as a “really scary time” for her.
An extra 30 minutes has been added to the running time of the investigative show, which will be screened on Monday evening and include the interview with Virginia Giuffre.
A BBC News Press Team tweet on Panorama’s official account said: “Change of timing for next week’s @BBCPanorama, as the programme is now an hour long. The Prince and the Epstein Scandal will now air at 9pm on @BBCOne on Monday 2 December.”
It is not known why the programme has been extended as the BBC declined to comment.
Andrew’s attempts to defend himself against Giuffre’s accusations and explain his friendship with Epstein, a convicted sex offender, in a BBC Newsnight interview failed dramatically.
The duke has withdrawn from public duties after he was widely criticised for failing to show remorse for his friendship or much empathy with Epstein’s alleged victims during his television appearance.
He has resigned from a large number of patronages or seen organisations he was once involved with sever ties.
Giuffre has claimed in court papers in Florida that she was forced to have sex with Andrew when she was aged 17, under 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”.
Buckingham Palace has branded the allegations “false and without any foundation”, stating: “Any suggestion of impropriety with under-age minors” by the duke was “categorically untrue”.
Epstein was found dead on August 10 in his prison cell in New York, where he was being held on sex trafficking charges.