Speaking at the charity gala on Wednesday night, the Duke of Cambridge explained to referee Shirley Ballas and hostess Claudia Winkman that Kate was a "huge fan".
Speaking to the couple, the Duke of Cambridge said he had seen the play.
He continued: “I watched the play [Strictly] several times.
Prince William added: "Catherine is a huge fan and my mother-in-law loves it."
Then Prince William joked with them about what he wanted to see change.
He said, "Why does Claudia never dance?"
Claudia then unusually replied, "I'm too high!"
The news of the Duchess's delight comes after she was revealed this week that she and Prince William are using a clever trick to reduce the amount of photos taken by the pair.
As the Duchess entered the royal family, Kate spent much of her time in front of the camera.
Although she will always look ready for pictures, Kate and William are reportedly not huge fans of photography.
One royal correspondent who spoke to The Venice Fair explained: "Kate and William, in particular, are known for deliberately not looking at a particular point when photographed – making it difficult for photographers to get good pictures of them."
By doing so, the pair allegedly reduce the amount of media attention they receive.
YES TO: Prince Harry and Prince William fix charity royalties for charity
Although her children will appear in official photo calls, Kate is a beloved photographer herself and uses the opportunity to publish her own family photos.
Royal could choose to do so to control what is seen and to reduce the amount of copyright being photographed in public.
The show's director at Baby Show, said Zoe Bonser Express.co.uk: "Usually Kate takes a photo of herself, giving the freedom and power over what is used in public – and the chance to use her art skills."
Kate was recently awarded an honorary lifetime membership of the Royal Photographic Society.
Dr Michael Pritchard, chief executive of RPS, said: "The Duchess of Cambridge has a longstanding interest in photography and its history.
"She is the last in a long line of royal photographers and society is pleased to recognize her talent and enthusiasm through honorary membership.
"We look forward to a continued relationship with her."