Minnelli, who was to begin shooting next week, was advised by her doctor to stay off of her ankle following a minor injury. She plans to make a future appearance on the show.
The Tony winner signed on to play the agent of actress Victoria Chase, played on the series by Wendie Malick. A replacement for her character, Jacki, has not yet been announced.
"Hot in Cleveland" also stars Valerie Bertinelli, Jane Leeves and Betty White.
Minnelli was last seen on Broadway in Liza's at the Palace…, which received a Tony Award in 2009 for Best Special Theatrical Event. The singer-actress took home the Tony Award for Best Actress in a Musical in 1965 for Flora the Red Menace and again in 1978 for her performance in The Act. She also won a special Tony Award in 1974 "for adding lustre to the Broadway season." Minnelli is also a Golden Globe, Oscar and Emmy Award-winning actress. Her film credits include "The Sterile Cuckoo," "Arthur," "New York, New York" and "Stepping Out."
"Hot in Cleveland" airs Wednesday nights at 10 PM ET on TV Land.