The Amazonia Arena is one of the five stadiums planned for this year's tournament that have not been completed.
"One year ago there were doubts over whether Manaus would be ready for the Cup," Valcke said as he visited the riverside city located some 1,900km north-west of the capital Brasilia.
"We worked jointly with the organising committee and the governments and we were successful. Today I can say that the project is one of the nicest, it is a fantastic project."
Construction on the stadium is 97 percent done, and builders say it will be ready for delivery by early March.
Booming Brazil is gearing up to host the World Cup amid fears its infrastructure for playing and hosting are not ready for prime time, and amid public safety concerns.
The tournament starts in Sao Paulo on June 12, and ends on July 13.
On Friday a construction worker was killed in the Arena, the third fatal accident to hit the venue and the sixth worker killed in Brazil while building a World Cup stadium.
Once a thriving town during the rubber boom of the late 19th century, Manaus was a controversial choice for a new stadium in part because there is no top area club to attract fans after the World Cup.
Four first round World Cup games are scheduled to be played at the Amazonia Arena, including England-Italy on June 14.
That match will be "one of the most important games of the first round," Valcke said. "This could be a final Cup game."
The other first-round games to be played in Manaus are Cameroon-Croatia on June 18, the United States-Portugal on June 22, and Honduras-Switzerland on June 25.
Valcke, who is visiting World Cup sites across Brazil, will also visit Brasilia and Porto Alegre before travelling to the southern city of Florianopolis.
FIFA originally set a deadline of December 31 for all stadiums to be ready, but was forced to drop it with six venues still unfinished at that stage.
Valcke has already warned that another of Brazil's 12 venues, Curitiba, faces being dropped from the World Cup if it cannot show by Tuesday that the venue, whose construction has been lagging behind schedule, is back on track.
