Footage shows the building crumbling to the ground after it exploded in a huge ball of fire and smoke.
More than 150 firefighters battled the blaze that raced through the São Paulo building, a former federal police headquarters, but it eventually collapsed in a massive conflagration.
The newspaper reported that the military had joined the rescue effort, and was attempting to extract a person from the upper floors of the building through an adjacent property when the structure collapsed.
There have been unconfirmed reports that there were people on the top floors when the building collapsed. According to authorities, 400 people were registered as living in the building, which belonged to the government. Firefighters evacuated the building and contained the fire with no victims or risk of collapse. Firefighters set up a perimeter and worked to evacuate people.
At least one person died and three others were missing, a fire department spokesman said.
"Happily the majority got out", he said, adding that residents believed the blaze may have been sparked by a gas leak.More news: Were Analysts Bearish Halfords Group plc (LON:HFD) This Week?
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Flabio Gabia, who works near the building, told Estadao: "When I went to see what it was, the streets were filled with desperate people".
The governor said it was legally hard to force people to evacuate the old and decaying buildings.
Officials say it will take days to clear the debris.
Doria argued the downtown should showcase Sao Paulo, the engine of Brazil's economy and one of the hemisphere's most important financial centers. The disaster is sure to renew attention on squatters and abandoned buildings.
First responders are using dogs and removing rubble by hand in the hope of finding survivors, the Sao Paulo Fire Department tweeted.