The accident in Sao Paulo could delay the handover of the stadium to football’s world body FIFA which called for all 12 venues to be ready by December.
The Itaquerao Stadium was practically completed before the collapse.
A huge metal structure buckled on top of the stadium, destroying part of the stands in the east side of the venue. A LED panel installed outside the venue also was hit.
Firefighters said at least three people died in the accident, which apparently happened when a crane collapsed on top of the metal structure.
Corinthians, the club that will move into the new stadium, said in a short statement that it “deeply regrets the accident”.
The stadium will seat nearly 70,000 people for the World Cup opener on June 12. The venue is scheduled to host another five matches, including a semifinal.
It was initially expected to be built for the Confederations Cup this year, but delays with financing for the venue prompted authorities to scrap the stadium from the World Cup warm-up tournament.
Fifa President Sepp Blatter said he was “deeply saddened by the tragic deaths”.
Fifa 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 per cent ready.
Six of Brazil’s stadiums – including Itaquerao – are not yet ready for the World Cup next summer.
Construction problems and public protests about the money being spent have delayed the preparations.
On Tuesday, Danny Jordaan, who was behind South Africa’s preparations for the 2010 World Cup, said Brazil might have to start round-the-clock construction work to get things ready.