Comic Peter Serafinowicz will play artist Warhol in the programme Hey Diddly Dee, which is directed by Hustle actor Marc Warren.
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.
It 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.