Ms. Bueno was the first and so far the only female player from South America to win the Wimbledon singles title and is one of only eight women to win at least three championships at both Wimbledon and the U.S. Open.
The 9 de Julho Hospital said she had been admitted for "oncological treatment" and asked for privacy.
Bueno said men were key to her game.
However, her career was cut short by elbow problems, which she blamed on the heavy rackets used in the sport at 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".
In 1959, Ms. Bueno became the first non-American in more than 20 years to win the women's title at Wimbledon, defeating Californian Darlene Hard in straight sets, 6-4, 6-3. A national hero in her native Brazil, Bueno also had a special flair that probably cannot be taught.
World No. 1 in 1959, 1960, 1964 and 1966, Bueno was Brazil's best ever player, winning 19 Grand Slam titles. She grew up across the street from a tennis club, where her parents played.
She took the Wimbledon singles title again in 1960 and 1964.
"We send our condolences to the friends and loved ones of Maria Bueno, a four-time #USOpen singles and doubles champion". She later became a leading tennis commentator on Brazilian television.
One tennis writer, John Barrett, called her "the elegant queen of Brazilian tennis". The hospital released a statement on Friday afternoon confirming her death, but declined to provide more details out of respect for her family.
On and off the court, Bueno "always showed a lot of fight", Brazilian tennis player Bia Haddad said.
Bueno was a consultant for several years for Sportv and commented on matches with Gustavo "Guga" Kuerten, the other Brazilian tennis legend.