She graduated from Howard University, where she later taught drama, and is a member of the sorority Alpha Kappa Alpha. Rashād first became notable on the stage with a string of Broadway credits, including Deena Jones in Dreamgirls (she was Sheryl Lee Ralph's understudy until she left the show in 1982 after Rashad was passed over as Ralph's full-time replacement) and playing a Munchkin in The Wiz. In 1978, she released the album Josephine Superstar, a disco concept record telling the life story of Josephine Baker. The album was mainly written and produced by Jacques Morali and Rashād's one-time husband Victor Willis, lead singer and lyricist of the Village People. Rashād received another career boost when she joined the cast of the ABC soap opera One Life to Live in 1983.
Rashād is best known for another television role, that of attorney Clair Huxtable on the NBC sitcom The Cosby Show. The show starred Bill Cosby as obstetrician Cliff Huxtable, and focused on their life with their five children.
When Cosby returned to TV comedy in 1996 with CBS's Cosby, he called on Rashād to play Ruth Lucas, his character's wife. The pilot episode had been shot with Telma Hopkins, but Cosby then fired the executive producer and replaced Hopkins with Rashād. The sitcom ran from 1996 to 2000. That year, Cosby asked Rashād to work on his animated television series Little Bill, in which the actress voiced Bill's mother, Brenda, until the show's end in 2002.
In 2003, she was honored as Woman of the Year by the Harvard Black Men's Forum. In 2005, Rashād received an honorary Doctor of Fine Arts (D.F.A.) degree from Brown University. She played Kill Moves' mother on Everybody Hates Chris on Sunday, December 9 2007.
In 2008, she appeared in the television adaptation of A Raisin in the Sun. She currently stars on Broadway as Big Mama in an all-African American production of Tennessee Williams's Pulitzer Prize-winning drama Cat on a Hot Tin Roof directed by her sister Debbie Allen. She appears alongside stage veterans James Earl Jones (Big Daddy) and Anika Noni Rose (Maggie), as well as film actor Terrence Howard, who makes his Broadway debut as Brick.