Borussia Dortmund's Mario Gotze, who scored the goal to win Germany the World Cup in 2014, has been omitted by Low.
Loew took over after the 2006 World Cup in Germany and has led his country to at least the semi-finals in all of the five major tournaments for which he has been at the helm.
"I feel a great desire for the upcoming World Cup in Russian Federation and the intense weeks with the team", said Low.
But manager Joachim Low, who has extended his contract to 2022, names the world-class keeper along with Barcelona's Marc-Andre ter Stegen, Bayer Leverkusen's Bernd Leno and PSG stopper Kevin Trapp.
Bayer Leverkusen's Julian Brandt and Leon Goretzka, who will join Bayern from Schalke in the summer, are budding stars tipped to make a name for themselves on the worldwide stage as well.
Joachim Löw has opted to go for form over sentiment, as both Mario Götze and Andre Schürrle - the two men who combined to score the solitary victor in the final of the 2014 World Cup - have been left out.
While most fans will be content with MATS starting, Neuer is more critical to the core of the team as captain, and that will play a major role in the decision. My job as national coach is sometimes to drop a bombshell on some players' dreams. The 30-year-old Wagner has scored four goals in his eight internationals and was part of last year's Confederations Cup-winning team.
Borussia Dortmund forward Marco Reus is included after missing both the 2014 World Cup and Euro 2016 through injury.
They face Sweden in Sochi six days later before rounding off their Group F campaign against South Korea in Kazan. "But this season he didn't play at his highest level".