Low's entire backroom staff have also agreed new deals, as has national team managing director Oliver Bierhoff.
Neuer, who has played in five games this season having broken a metatarsal in September, is one of four goalkeepers named in Low's provisional squad, with Barcelona's Marc-Andre ter Stegen seen as the man most likely to start following Neuer's injury problems. Preparations at its training camp in South Tyrol, Italy, begin on May 23.
"We saw that we're not as good as we're always told we are - and perhaps some of us think we are".
Arsenal star Mesut Ozil, Real Madrid midfielder Toni Kroos and Bayern Munich trio Mats Hummels, Thomas Mueller and Jerome Boateng are part of Germany's 27-man provisional list for the 2018 FIFA World Cup in Russian Federation.
Aside from the likes of Ilkay Gundogan, Sami Khedira, Toni Kroos, Julian Draxler and Mesut Ozil, there are also still places at stake in Germany's midfield - an area of considerable strength.
Uncapped Freiburg striker Nils Petersen is rewarded for a fine goalscoring season in the Bundesliga Mario Gotze who scored the winning goal in the final as Germany triumphed four years ago, misses out, however, after suffering a severe dip in form at Signal Iduna Park this term but Arsenal defender Shkodran Mustafi and Liverpool midfielder Emre Can are among those to miss out.
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. Bayern striker Sandro Wagner misses out on the tournament as Loew favored Stuttgart striker Mario Gomez.
Ozil and Gundogan have been criticised by the German Football Federation (DFB) for posing in photos with Turkish president Recep Tayyip Erdogan.
"That's why it's not good that global players allow themselves to be manipulated for his electoral campaign".