"But clearly we can expect something to happen during the event," he conceded.
"And why couldn't something similar happen until 2016, when the international press will be here?," he added, referring to the Rio Summer Olympics.
Brazil has been rocked by nationwide street protests for more than two weeks, as hundreds of thousands of citizens demand better social services and an end to rampant corruption.
They are also questioning why the country is investing $15 billion in the ongoing Confederations Cup and the World Cup when social programs such as education and health are underfunded.
Some of the protesters have criticized what they see as the excessive influence of FIFA, world's football governing body, in the organization of the two sporting events.
Valcke said that while protests are "part of the democratic system... this does not mean people should not go to the (World Cup) stadiums."
He stressed some of the infrastructure built for the World Cup, notably transport systems, would benefit the Brazilian people.