Fontaine died "very peacefully" in her sleep of natural causes, Beutel said. She was in her Carmel, California, home.
She is survived by her older sister, actress Olivia de Havilland -- with whom she had not spoken for decades.
Fontaine was born Joan de Beauvoir de Havilland in 1916 in Tokyo, Japan, where her British father was a patent lawyer and teacher. She and her sister moved to Saratoga, California, with their mother in 1919 when her parents separated.
Fontaine was a teenager when she began her acting career as Joan Burfield in the 1935 film No More Ladies. She later adopted the stage name Fontaine -- the name of her mother's second husband.
She wrote in her 1978 autobiography, "No Bed of Roses," that her mother, who was an actress, began encouraging the rivalry with her older sister at an early age.
The feud extended to their careers when both sisters were nominated for best actress Oscars in 1942. Fontaine, who was nominated for Alfred Hitchcock's "Suspicion," beat her sister Olivia de Havilland, who was nominated for "Hold Back the Dawn."