The singer, who is said to be devoting more time to the acting side of her career, will appear in an edition of Playhouse Presents ... on the Sky Arts channel.
It revolves around a group of actors putting on a production about US art guru Warhol, with Minogue playing a Sedgwick-style figure called Bibbi, and will be screened on March 14.
Minogue, 44, said: "When the script was sent to me, I read it and knew instinctively I wanted to be part of this project. In Hey Diddly Dee, Marc has created a beautiful and quirky story."
The Australian has appeared in a number of movies including the recent Holy Motors, as well as taking TV roles such as a Doctor Who Christmas special.
Matt Smith, who plays the BBC1 time lord, will also make his directorial debut later in the Sky Arts series.
He has made a film called Cargese, while Idris Elba - known for his performances in Luther and The Wire - has written and will direct another of the Playhouse Presents ... programmes, which will star Reggie Yates.
Turner Prize-winning potter and artist Grayson Perry is credited with co-creating another of the films, about a young transvestite.