The 57-year-old entertainer - who is currently going through a bitter divorce with fourth husband DAVID GEST - has signed up for six episodes of the wacky family comedy, which is executive produced by Ron Howard.
Minnelli's character is a widowed socialite who develops a crush on BUSTER, the show's neurotic student, and her contract could be extended if the ARTHUR actress agrees.
Minnelli enthuses, "I'm having such fun doing it because I'm finally allowed to use my comic ability. When Ron Howard called me I was so surprised. He said, 'How would you like to do a couple of shows and see how you like it? You could be anyone you want to be. We'll figure it out.'"