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."
De Havilland won the first of her two Oscars in 1947 when she was given the best actress award for "To Each His Own." De Havilland and Fontaine remain the only sisters who have best-actress Academy Awards.
The long-standing feud with de Havilland was at such a peak during one Oscar winners' reunion in 1979 that they had to be seated on opposite ends of the stage.
"I was shocked and saddened to learn of the passing of my sister, Joan Fontaine ... and I appreciate the many kind expressions of sympathy that we have received," a statement released by Olivia de Havilland to CNN said.
Fontaine, at 23, was the youngest best actress Oscar winner at the time she was given the award for "Suspicion." Her Oscar represents the only one ever won by a Hitchcock film.
Her first Oscar nomination came in 1941 for her role in Hitchcock's "Rebecca." A third nomination followed in 1943 for "The Constant Nymph."
Fontaine married four times: to Brian Aherne in 1939, William Dozier in 1946, Collier Young in 1952 and Alfred Wright, Jr. in 1964. While three of the marriages lasted less than five years, the marriage to Young lasted nine years. She had a daughter with Dozier and adopted a girl while married to Young.
Fontaine acted on the Broadway stage in "Tea and Sympathy" in 1954.
She received a Daytime Emmy nomination for outstanding guest appearance in the daytime soap opera RYAN'S HOPE in 1980.
Her other TV credits included BARE ESSENCE, HOTEL and THE LOVE BOAT.
Check out a clip of Fontaine on RYAN'S HOPE below: