The organization insisted safety remains its top priority, while the Brazilian club also extended its sympathy following the death of three workers.
The stadium was nearing completion before a crane fell and destroyed a section of the ground, causing it to collapse and casting doubt as to whether it will be ready in time for next summer's tournament.
FIFA president Sepp Blatter extended his condolences to the families of those who had been killed by the stadium accident on Twitter, while the organization that he heads insisted that safety is its number one priority.
"FIFA and the LOC have learned of the death of workers at the Corinthians Arena site in Sao Paulo with great sadness," FIFA wrote on its website. "We wish to send our heartfelt condolences to the family of the workers who tragically died today. The safety of workers is the top priority for FIFA, the LOC and the federal government.
"We know the safety of all workers has always been paramount for all the construction companies contracted to build the 12 World Cup stadiums. The Department of Labor and the local authorities will fully investigate the reasons behind such a tragic accident. Please understand that we are in no position to comment further at this stage, as we are awaiting further details from the authorities."
This is the third fatal incident in the building of World Cup 2014 stadia - the first at the Estadio Nacional Mane Garrincha in June 2012 and the second in March this year at the Arena Amazonia, which both involved a worker falling from a height.
Corinthians also expressed its sympathy about the incident in a club statement.
However, Brazilian news outlet Folha alleges former club chairman Andres Sanchez, who was in charge of the stadium's construction, attacked one of its reporters outside the scene of the incident.