"There is not a single stadium ready today," Jerome Valcke said.
He added that beer must be allowed at matches, despite Brazilian law prohibiting beer sales at games.
Brazil's World Cup will be played in 12 far-flung venues, including a 44,000-seat stadium being built in the Amazon jungle city of Manaus.
All 12 cities will host at least four matches — triggering concerns about travel chaos in the massive nation, whose ailing airport infrastructure has repeatedly been highlighted by FIFA as needing an upgrade.
Valcke also said that FIFA and Brazil need to resolve a long-standing dispute over ticket prices soon.
As part of his latest trip to Brazil to check on the progress of the hosts' preparations, Valcke urged the Brazilian Congress to approve a pending package of laws regulating the World Cup.
Brazil prohibited alcohol sales inside stadiums in 2003 in a bid to cut down on violence, but the Budweiser beer company is a major World Cup sponsor and FIFA is advocating that beer sales be allowed in the stadiums during the World Cup.
"We're not talking about alcohol, we're talking about beer," Valcke said.