Details of her death were not immediately available.
In addition to playing a mousey spouse in both the Hitchcock films, first alongside Laurence Olivier and then to Cary Grant, Fontaine's other well-known movies included 1943's The Constant Nymph, which got her a third Oscar nomination, 1944's Jane Eyre with Orson Welles, 1952's Ivanhoe with Robert Taylor, and 1957's controversial Island in the Sun with Harry Belafonte.
Her final role was in a 1994 TV movie.
Born Joan de Beauvoir de Havilland in Tokyo to British parents, Fontaine recalled for PEOPLE in 1978: "My mother, Lilian de Havilland ... was beautiful, gracious and a talented actress. My father was an English professor at Waseda and Imperial universities in Tokyo who left Mother for our Japanese maid when I was 2. My mother later married a department store manager, George Milan Fontaine, but she remained the dominant figure in our lives."
While her older (by one year) sister, Olivia de Havilland, best known for playing Melanie in Gone with the Wind, sought an acting career, Joan studied at the American School in Tokyo before joining de Havilland in Los Angeles, where she too got a screen test.
Among Fontaine's earliest roles were in 1939's all-star The Women at MGM, and with Cary Grant that same year, in RKO's Gunga Din.
Hollywood's Most Famous FeudAt some point, however, her relationship with her sister shattered, and the two remained archenemies until Fontaine's dying day.
De Havilland, at 97, continues to live in Paris. One theory about their rift is that it was caused by Fontaine's winning the Oscar over De Havilland's nomination for the tearjerker Hold Back the Dawn.
Neither sibling would ever provide a reason for their feud.
"I regret that I remember not one act of kindness from Olivia all through my childhood," Fonataine told PEOPLE. "One of my earliest memories is when she was 6 and I was 5. She had learned to read and, one night when we were alone, she read aloud the Crucifixion from the Bible with mounting gusto until finally I screamed. Olivia loved it. One July day in 1933 when I was 16, Olivia threw me down in a rage, jumped on top of me and fractured my collarbone."
Pressed to explain the rivalry, Fontaine could only say, "One person called our relationship paranoid – but he didn't say on whose part. Not mine, though I may have a persecution complex. There must be some explanation. Olivia so hated the idea of having a sibling that she wouldn't go near my crib."
Fontaine lived out her days in Carmel, Calif. She had two children from her four marriages. Her husbands were actor Brian Aherne, TV producer William Dozier, producer Collier Young and journalist Alfred Wright Jr.
All her marriages ended in divorce.
In her PEOPLE interview, Fontaine, who now leaves her sister as one of the last survivors of Hollywood's Golden Age, spoke of how she wanted to die.
"At age 108," she said, "flying around the stage in Peter Pan, as a result of my sister cutting the wires. Olivia has always said I was first at everything – I got married first, got an Academy Award first, had a child first. If I die, she'll be furious, because again I'll have got there first!"