Charisse was admitted to Cedars-Sinai Medical Center on Monday after suffering an apparent heart attack, said her publicist, Gene Schwam.
She appeared in dramatic films, but her fame came from the Technicolor musicals of the 1940s and 1950s.
Classically trained, she could dance anything, from a pas de deux in 1946's "Ziegfeld Follies" to the lowdown Mickey Spillane satire of 1956's "The Band Wagon" (with Astaire).
The 1952 classic "Singin' in the Rain" marked a breakthrough.
When Freed was dissatisfied with another dancer who had been cast, Charisse inherited the role and danced with Kelly in the "Broadway Melody" number that climaxed the movie. She stunned critics and audiences with her 25-foot Chinese silk scarf that floated in the air with the aid of a wind machine.