Bueno won 19 major titles during her career in the 1950s and 60s, including three Wimbledon singles titles and four US championships.
She had recently been admitted to hospital suffering from mouth cancer.
A self-taught prodigy, she brought grace to the game and was a dominant force, BBC Americas editor Leonardo Rocha writes.
However, her career was shortened by elbow problems, which she blamed on the heavy wooden rackets of the time.
Brazilian President Michel Temer has led tributes to the star, tweeting that she would be remembered as “the number one of tennis in the hearts of all Brazilians”.
Born in the city of Sao Paulo, Maria Esther Bueno made history as the first South American woman to win the Wimbledon singles title.
Despite having no formal coaching in her teenage years, she swept the Brazilian scene before gaining international acclaim by winning the Italian Championships in 1958, beating the best English and Australian players.
She went on to win the Wimbledon doubles that same year alongside American Althea Gibson.
Bueno then took her first Wimbledon singles title in 1959, along with the US championship title, becoming the world number one and earning her the Associated Press Female Athlete of the Year award.
As she received the award, she said: “I’m not good, I’m afraid of everyone I play.”
She took the Wimbledon singles title again in 1960 and 1964.
In 1965, Bueno again won the Wimbledon doubles title, this time with tennis partner Billie Jean King.
She was labelled the “Sao Paulo Swallow” for her ability to dominate the net by former BBC Sport commentator John Barrett.
Retiring from the sport in 1977, she became a commentator herself for the Brazilian channel SporTV.
Bueno was admitted to a hospital in Sao Paulo on Tuesday. On Friday the hospital released a statement confirming her death but declined to provide further details.