Her son, Peter H David, made the announcement in a newsletter to her fans, saying she died "a few days ago".
In 1947 she was the highest-paid star in the United States. But she retired from the business the following year when she was just 27.
Durbin made her film debut in the 1936 MGM short Every Sunday, in which she appeared alongside Judy Garland.
Born Edna Mae Durbin in Winnipeg, Canada in 1921, Durbin was nurtured and promoted by producer Joe Pasternak.
Her first movie for the Universal studios, Three Smart Girls, was nominated for the best picture Oscar in 1937.
Durbin auditioned for the part of Snow White in 1936. But Walt Disney turned her down, saying her 15-year-old voice was too mature for the part.
In 1939, Durbin and fellow teen star Mickey Rooney were presented with Juvenile Academy Awards for their "significant contribution in bringing to the screen the spirit and personification of youth."
The success of her films, which reportedly saved Universal from bankruptcy in the late 1930s, was estimated to account for 17% of the studio's revenue during the decade.
In 1946 Durbin's salary of $323,477 made her the second highest-paid woman in America, just behind Bette Davis.
Winston Churchill watched her films before they were released to the general public in the UK, while Anne Frank hung a picture of Durbin on the wall of the attic in which she and her family hid from the Nazis.
In 1949, after 21 films and at the height of her worldwide fame, Durbin quit the movie business and retired to a village in France.
She shunned the spotlight with her third husband, the film director Charles David, who died in 1999.
Durbin rarely gave interviews but did send reporters a letter in 1958 in which she said she was "never happy making pictures".
"The character I was forced into had little or nothing in common with myself - or with other youth of my generation, for that matter."
Deanna Durbin, one of Hollywood's biggest box-office stars in the 1930s and early '40s, has died aged 91.