A large plume of smoke billowed from the Latin America Memorial, a cultural centre which hosts an art gallery, an auditorium and other facilities.
At least 15 firefighters were injured as dozens of crews went to the scene.
Oscar Niemeyer, who was behind some of the 20th Century’s best known modernist buildings, died a year ago aged 104.
He designed the main government buildings in the futuristic capital, Brasilia, developing a style defined by sweeping curves and stark concrete.
The Latin America Memorial, built in the west of Sao Paulo in 1989, was empty at the time of the fire and authorities say no members of the public were hurt. The cause of the fire is unclear.
Fire first swept through the 1,600-seat Simon Bolivar auditorium at the complex at around 15:00 local.
While the extent of the damage was unclear, there were fears for some of the art works at the complex.
A spokesperson told reporters that a giant tapestry by Brazilian artist Tomie Ohtake may have been partially destroyed.
Another building in the complex hosted the Latin American Parliament from 1992 to 2007. The parliament is now based in Panama.
The Latin America Memorial comprises several buildings in an area of more than 84,480 sq m (101,376 sq yards) and was designed by Oscar Niemeyer and conceived by the anthropologist Darcy Ribeiro.
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