Parker played the lady friend of Captain Von Trapp in the film, who loses Von Trapp to Julie Andrews' character Maria.
The actress died on Monday morning due to complications from pneumonia at a medical facility near Palm Springs, California, reported Variety.
Parker earned three Oscar nominations for best actress for her roles in 'Caged', 'Detective Story' and 'Interrupted Melody'.
Parker was born in Cedarville, Ohio. After high school in Cleveland, she moved to California, where she studied at the Pasadena Playhouse.
Also Read
She appeared in films like 'Of Human Bondage', 'Never Say Goodbye', 'Escape Me Never' and 'The Woman in White', 'Scaramouche', 'The Naked Jungle and 'The Man With the Golden Arm' with Frank Sinatra.
Parker had an equally impressive career in TV beginning late 60s where she starred in 'Bracken's World', 'The Man From UNCLE', 'The Love Boat', 'Fantasy Islan', 'The Eleventh Hour' and 'Murder, She Wrote'.
Her last screen appearance was in the 1991 telepicture 'Dead on the Money'.