A senior local fire official said crews were called to the Arena Corinthians after reports of a collapsed crane.
It fell on top of a metal structure, destroying parts of a stand.
The arena was due to be completed at the end of December to meet a FIFA deadline. Brazil has admitted it is struggling to have all 12 venues ready.
TV footage showed the huge metal structure buckled on top of the stadium, which is also known as Itaquerao.
Part of the stand – believed to be in the southern sector – was damaged. A LED panel outside the venue was also hit.
Rescue teams are checking the site to see if there are more victims.
Corinthians, the club that will move into the new stadium, said in a short statement that it “deeply regrets the accident”.
FIFA President Sepp Blatter said he was “deeply saddened by the tragic deaths”.
Secretary General Jerome Valcke said: “Extremely shocked by the news from Sao Paulo. Our thoughts are with the families of the victims of this accident.”
The venue is being built by Brazil’s Odebrecht company, who recently said the arena was about 94% ready.
Six of Brazil’s stadiums – including Itaquerao – are not yet ready for the World Cup next summer.
VGF3PBEDjUMAt least five people, including a four-month-old baby, have been killed after dozens of tornadoes…
Harvey Weinstein has been hospitalized just days after his 2020 rape conviction in New York…
Hamas has published a video showing the first proof of life of US and Israeli…
Prosecutors and Donald Trump’s attorneys delivered opening statements and the first witness was called on…
The House of Representatives has finally approved $61 billion in new US military aid for…
The real estate market in the United States has always been a gauge for economic…