FIFA has selected 12 Brazilian cities to hold games at the next World Cup, but Valcke says the sole candidate country for 2014 was already falling behind deadlines.
"I got a report on the status quo of the Brazilian stadiums. I have to say it is not very nice," Valcke said. "There are a number (of stadiums) with red lights already, which is amazing. It is amazing how Brazil is already late. And I am not just talking about Morumbi or Maracana stadiums, I am talking about a number of stadiums.
"The stadiums are the basic points we need to have a World Cup and in Brazil, for the time being, most of the deadlines are already over and we have to work on new deadlines."
Valcke said he received the report Monday morning, just hours before a ceremony at Johannesburg's Soccer City stadium - the venue for the 2010 final - to celebrate the host's stadium construction. He later thanked workers for their role in preparations.
FIFA will now have little time to celebrate South Africa's readiness before focus shifts to Brazil, which will host football's showpiece event for the first time since 1950.
"For the time being, we have 12 host cities and we are not in a period where we have to make decisions," Valcke said. "What we are saying is that all the things they have promised, they have been saying and they have signed, the commitment from different people - they have to deliver these commitments."
Valcke also warned that if the stadium in Brasilia was reduced to 30,000 seats, as reports suggest, it will not be allowed to host the tournament's opening game.
The FIFA secretary general, who has constantly played down worries over South Africa's readiness, said Brazil is experiencing similar troubles to the African country.
"Brazil is showing it is very difficult to organise a World Cup in Brazil, as it was difficult in South Africa," he said.
In a statement, the local organising committee in Brazil said it will evaluate all stadiums beginning on Thursday. The visits will last until May 20, and will also look at the construction schedule at each venue.