The singer turned actress starred in films such as Calamity Jane and Pillow Talk and had a hit in 1956 with Que Sera, Sera (Whatever Will Be, Will Be).
Her screen partnership with Rock Hudson is one of the best-known in the history of romantic movies.
In a statement, the Doris Day Animal Foundation said she died on Monday at her home in Carmel Valley, California.
It said she had been "in excellent physical health for her age, until recently contracting a serious case of pneumonia".
"She was surrounded by a few close friends as she passed," the statement continued.
Born Doris Mary Ann Von Kappelhoff in April 1922, Day originally wanted to be a dancer but had to abandon her dream after breaking her right leg in a car accident.
Instead she began her singing career at the age of 15. Her first hit, Sentimental Journey, would become a signature tune.
Her films, which included Alfred Hitchcock's The Man Who Knew Too Much and That Touch of Mink, made her known around the world.
But she never won an Oscar and was nominated only once, in 1960, for Pillow Talk, the first of her three romantic comedies with Hudson.
Honours she did receive included the Presidential Medal of Freedom in 2004 and a lifetime achievement Grammy in 2008.
Her last release, the compilation album My Heart, went to number one in the UK in 2011.
Day's wholesome, girl-next-door image was a popular part of her myth that sometimes invited ridicule.
"I've been around so long, I knew Doris Day before she was a virgin," the musician Oscar Levant once remarked.
Day herself said her "Miss Chastity Belt" image was "more make-believe than any film part [she] ever played."
Her life was certainly not as sunny. She married four times, was divorced three times and was widowed once.
She also suffered a mental breakdown and had severe financial trouble after one husband squandered her money.
In the 1970s, she turned away from performing to focus her energies on her animal foundation.
According to the organisation, she wished to have no funeral, memorial service or grave marker.