Parker was born on August 2, 1964 in Fort Jackson, South Carolina. The youngest of four children, she is the daughter of Caroline Louise (née Morell) and John Morgan Parker, a judge who served in the U.S. Army. Her ancestry includes Swedish (from her maternal grandfather), English, Scottish, Scots-Irish, German, and Dutch. Because of her father's career, Parker spent parts of her childhood in Tennessee and Texas, as well as in Thailand, Germany, and France. She described her childhood as “profoundly unhappy”, further noting that, “My parents did everything they could; I had books, clothes, a home and a warm bed, but I was never happy”. She graduated from Marcos de Niza High School in Tempe, Arizona. Parker majored in drama at the North Carolina School of the Arts, where she met Joe Mantello, and graduated in 1986.
Parker got her start in a role on the soap opera Ryan's Hope. In the late 1980s, Parker moved to New York, where she got a job measuring feet at the ECCO shoe company. After a few minor roles, she made her Broadway debut in a 1990 production of Craig Lucas' Prelude to a Kiss, playing the lead role of Rita. She moved with the production when it transferred from its origin Off-Broadway. She won the Clarence Derwent Award for her performance and was nominated for a Tony Award (although she did not play the role when the film was made).
She starred with Kevin Kline in Grand Canyon (1991); with Kathy Bates, Mary Stuart Masterson, and Jessica Tandy in Fried Green Tomatoes (1991); with Susan Sarandon and Tommy Lee Jones in The Client (1994); with John Cusack in Bullets Over Broadway (1994); and with Drew Barrymore and Whoopi Goldberg in Boys on the Side (1995), as a woman with AIDS. Her next role was in a movie adaptation of another Craig Lucas play, Reckless (1995), alongside Mia Farrow, followed by Jane Campion's The Portrait of a Lady (1996), which also starred Nicole Kidman, Viggo Mortensen, Christian Bale, John Malkovich and Barbara Hershey. In addition, she appeared alongside Matthew Modine in Tim Hunter's The Maker (1997).
On December 7, 2003, HBO aired an epic six-and-a-half hour adaptation of Tony Kushner's acclaimed Broadway play Angels in America, directed by Mike Nichols. Parker played Harper Pitt, the Mormon Valium-addicted wife of a closeted lawyer. For her performance, Parker received Golden Globe and Emmy awards for Best Supporting Actress in a Miniseries.
In 2005, she started on showtime's series “Weeds” as Nancy Botwin, a pot dealing widow.
Parker starred opposite Bruce Willis in the film RED, an adaptation of the comic book mini-series of the same name. The film was released on October 15, 2010. In 2011, Parker became the host for the tenth season of the PBS documentary series Independent Lens. In 2013 she played roles in both RED 2 and R.I.P.D. She appeared in the Broadway Manhattan Theatre Club production of the play The Snow Geese by Sharr White at the Samuel J. Friedman Theatre from October 24 through December 15, 2013. The play was directed by Daniel J. Sullivan and also starred Danny Burstein and Victoria Clark.