The Oscar winner passed away in her sleep on Sunday at her home in California.
Her long-time friend Noel Beutel said: "She was an amazing woman, she had such a big heart and she will be missed."
Fontaine had a bitter rivalry with her older sister, Gone With The Wind star Olivia de Havilland.
It was fuelled by the fact that Fontaine often achieved success first - she was the first to marry, the first to win a large movie contract and the first to win an Oscar.
The star's career spanned four decades and some four dozen films, including the Hitchcock thriller Suspicion, for which she won an Academy Award in 1942, edging out her sister, who won one later.
By winning this award, she became the only performer, actor or actress, ever to win an Academy Award for a starring role in one of Hitchcock's many movies.
De Havilland, who is 97, was nominated that year for Hold Back the Dawn, which won two Oscars. They are only siblings ever to both win Oscars for acting.