Latimes.com reports that her son, actor Paul Clemens, confirmed her death. She died Monday.
A versatile character actress, she appeared in more than three dozen movies and was nominated three times for Academy Awards.
Parker brought a coolness, reserve and elegance to her portrayal of the baroness who is determined to marry the handsome captain played by Christopher Plummer, only to lose him to his children's governess, Maria, portrayed by Julie Andrews.
"Eleanor Parker was and is one of the most beautiful ladies I have ever known," said Plummer in a statement Monday.
"I hardly believe the sad news for I was sure she was enchanted and would live forever," he added.