Fontaine - the sister of fellow Oscar-winner Olivia de Havilland - died in her sleep on Sunday in her home in Carmel, her friend Noel Beutel said.
Born in Japan to British parents, she and her older sister moved to the US as children.
She won an Oscar as a vulnerable wife in the movie Suspicion in 1942.
Hitchcock also cast Fontaine in the lead role in his first Hollywood work, Rebecca.
Her other films included The Constant Nymph, Jane Eyre and Letter from an Unknown Woman.
Fontaine won her Oscar over her sister, who was in the running for her role in Hold Back The Dawn.
The pair's constant and lifelong rivalry was legendary in Hollywood.
De Havilland is still alive at the age of 97 and lives in Paris.
Fontaine gained another two Academy Award nominations, including for her lead role in Rebecca in which she played opposite Laurence Olivier.
The actress later said it was a "bittersweet moment" beating De Havilland to the best actress prize. "I was appalled that I won over my sister," she added.
But De Havilland - who played a significant role in Gone With The Wind - won two statuettes later in the 1940s for To Each His Own and The Heiress.
When she won the Oscar for To Each His Own in 1947, it is said she snubbed her sister's congratulatory gesture.
The sisters' difficult relationship continued for decades.
Speaking to the Hollywood Reporter in 1978, Fontaine said: "I married first, won the Oscar before Olivia did, and if I die first, she'll undoubtedly be livid because I beat her to it."
In her autobiography, the actress said: "I adore, respect and like my sister. But we don't seek out each other's company. We're such complete opposites."
The pair remain the only siblings to have both won Academy Awards for acting.
Fontaine - born Joan de Beauvoir de Havilland in Tokyo - had four marriages which ended in divorce. She held dual British-US citizenship.
She starred opposite many of the Hollywood greats, including as Joan Crawford's rival in her first major role in 1935's No More Ladies.
Fontaine also lined up with Katharine Hepburn, Fred Astaire and Cary Grant - her co-star in Suspicion.
The star was determined to play more wilful roles later in her career, gaining recognition for Tender is the Night in 1962.
Her final major screen appearance came four years later in The Witches, while her final screen credit was for the TV movie Good King Wenceslas in 1994.
Oscar-winning actress Joan Fontaine - the star of several psychological thrillers produced by Alfred Hitchcock - has died in California aged 96.