Parker died at a medical facility near her Palm Springs, California, home from complications related to pneumonia, according to director Richard Gale, who is a family friend.
Her acting career began on stage as a teenager, but it was a performance at the Pasadena Playhouse that led Warner Bros. to sign her to a studio contract on her 18th birthday.
She became a big screen leading lady during the 1940s, making her film debut in 1941 in "They Died with Their Boots On." Her early notable movies included "Pride of the Marines" in 1945 and "Voice of the Turtle" -- opposite Ronald Reagan -- in 1947.
The 1950s brought Parker to another level of stardom, including three best actress Oscar nominations.
The first Academy Award nomination came in 1950 for her portrayal of a terrorized prison inmate in "Caged." Parker was nominated again in 1951 for playing Kirk Douglas' wife in "Detective Story." A third Oscar bid followed in 1955 for her role as the polio-stricken opera star Marjorie Lawrence in "Interrupted Melody."
Despite a long list of other distinguished film roles -- including opposite Frank Sinatra in Otto Preminger's "The Man with the Golden Arm" (1955) and Clark Gable in "The King and Four Queens"(1956) -- it was a smaller role that audiences today are most likely to recognize.
Parker played the baroness who wanted to send the von Trapp children to a boarding school in the 1965 classic "The Sound of Music."
Although the stage and screen occupied the first several decades of her half-century acting career, she stayed busy working on television shows in the 1970s onward. She starred in NBC's "Bracken's World" in 1969. Her resume included three made-for-TV movies: ABC's "Once Upon a Spy" in 1980, NBC's "Madame X" in 1981 and TNT's "Dead on the Money" in 1991.
Parker also acted in a 1986 episode of CBS' "Murder, She Wrote."