Kane was born in Cleveland, Ohio, the daughter of Joy, a jazz singer, teacher, dancer, and pianist, and Michael Kane, an architect who worked for the World Bank. Her family is Jewish, and her grandparents emigrated from Russia. Her parents divorced when she was 12 years old. She attended the Cherry Lawn School, a progressive boarding school in Darien, Connecticut, until 1965. She also went to the Professional Children's School, in New York City, and made her professional theatre debut in a 1966 production of The Prime of Miss Jean Brodie, starring Tammy Grimes.
Kane portrayed Simka Dahblitz-Gravas, wife of Latka Gravas (Andy Kaufman), on the American television series Taxi, from 1981-83. She earned two Emmy Awards for her work in the series.
In 1984 Kane appeared in episode 12, season 3 of Cheers as Amanda, an acquaintance of Diane from the mental institution they both stayed at.
Kane was a regular on the 1986 NBC series All Is Forgiven, a regular on the 1990–91 NBC series American Dreamer, guest-starred on a 1994 episode of Seinfeld and had a supporting role in the short-lived 1996–97 sitcom Pearl.
In January 2009, she appeared in the TV series Two and a Half Men as the mother of Alan Harper's receptionist. In March 2010, Kane appeared in the TV series Ugly Betty as Justin Suarez's acting teacher. In 2014, she had a recurring role in the TV series Gotham as Gertrude Kapelput, Oswald Cobblepot's (Penguin's) mother.
In 2015, she was cast as Lillian, the landlord to the title character of Netflix's original series Unbreakable Kimmy Schmidt.
Kane also appeared in The Last Detail (1973), Annie Hall (1977), The World's Greatest Lover (1977), "Norman Loves Rose" (1982), Dog Day Afternoon (1975), The Princess Bride (1987) "Flashback" (1989) with Dennis Hopper, and Scrooged (1988), in which Variety called her "unquestionably [the] pic's comic highlight."
In 1998, she played Mother Duck on the cartoon movie The First Snow of Winter. In 1999 she made a cameo on the movie Man On The Moon as her character she played on Taxi.
Kane was nominated for an Academy Award for Best Actress for her role in the film Hester Street.
She starred in the off-Broadway play Love, Loss, and What I Wore in February 2010.
Kane made her West End debut in January 2011 in a major revival of Lillian Hellman's drama The Children's Hour, at London's Comedy Theatre. She starred alongside Keira Knightley, Elisabeth Moss and Ellen Burstyn.
In May 2012, Kane appeared on Broadway as Betty Chumley in a revival of the play Harvey.
Kane is known for her portrayal of the evil headmistress Madame Morrible in the Broadway musical Wicked, whom she played in various productions from 2005 to 2014.
Kane made her Wicked debut on the 1st National Tour, playing the role from March 9 through December 19, 2005. She then reprised the role in the Broadway production from January 10 through November 12, 2006. She again played the role for the Los Angeles production which began performances on February 7, 2007. She left the production on December 30, 2007, and later returned from August 26, 2008 until the production closed on January 11, 2009.
She then transferred with the L.A. company, to play the role once again, in the San Francisco production which began performances January 27, 2009. She ended her limited engagement on March 22, 2009. Kane returned to the Broadway company of Wicked from July 1, 2013, through February 22, 2014.This is My Night (Music Video) (1985) – Mimi in Chaka Khan's music video
Wicked (2005–2009; 2013–present) – Madame Morrible (Various productions)