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According to local media, Bueno died of a heart attack following a tennis match in Buzios, a beach resort on a peninsula east of Rio de Janeiro.
Brazil's richest healthcare billionaire, Bueno was worth US$3.1bn as of February, according to Forbes.
The son of a truck driver, Bueno started working as a shoeshine boy when he was 10. Known for being one of Brazil's most prominent self-made businessmen, he left his hometown of Guaranta, São Paulo, to study medicine at the Universidade Federal do Rio de Janeiro, where he became a surgeon.
During his studies, he worked at a failing medical clinic, which he bought in 1972, turning it into the largest private maternity hospital in the state of Rio de Janeiro in just five years.
Bueno then acquired other medical clinics, and founded Amil in 1978 with Pugliese.
Bueno also held shares in Dasa, the largest chain of medical diagnostic laboratories in Latin America, where his son, Pedro, was appointed CEO in December 2014 at the age of 24.