Day, who co-starred with 1950s and '60s superstars such as Rock Hudson and Cary Grant, died at her Carmel, California home after a bout with pneumonia, the Doris Day Animal Foundation said on its website.
A 2008 Vanity Fair article talked about Day's apparent insecurities, including confronting Hitchcock because she mistakenly thought he was unhappy with her work while filming The Man Who Knew Too Much.
While most people know her voice from clean-cut pop hits like Secret Love and the Oscar-winning Que Sera, Sera (Whatever Will Be, Will Be), Day's earlier records showcase a more sultry and inventive performer.
The statement added: "She was surrounded by a few close friends as she passed".
In 1948, she made her first film, Romance On The High Seas - the first of a string of hits that later included Calamity Jane, Love Me Or Leave Me and Please Don't Eat the Daisies.
"Doris Day was great actress & a lovely, gracious lady".
Day received a Presidential Medal of Freedom in 2004.
Melcher was Day's agent and "pulled her out of her Warner Brothers contract and revamped her as a freelance actress for hire", UK Telegraph reports.
The actress was married four times, to musicians Al Jorden (1941-1943) and George Weidler (1946-1949), film producer Martin Melcher (1951-68) and restaurateur Barry Comden (1976-1981).
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"Doris' wishes were that she have no funeral or memorial service and no grave marker", the statement concludes.
During her acting career, Day worked with some of the biggest stars and most well-known directors of the mid-century period, commonly known as the Golden Age of Hollywood. While recovering, Day accidentally discovered a hidden talent while singing along to the radio.
Born Doris Kappelhoff in Cincinnati, her stage name was even derived from a song - Helen Forrest's Day After Day. Instead, she turned to singing.
"Que Sera Sera", "Perhaps, Perhaps, Perhaps" and "Sentimental Journey".
The Doris Day Show: According to Justwatch.com, this sitcom originally broadcast on the CBS network from September 1968 until March 1973.
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Our thoughts are with her family and friends during this hard time.