The shot stopper picked up a knock in Bayern Munich's 2-1 German Supercup win over Borussia Dortmund at the weekend, and has consequently decided to withdraw from the squad for this week's friendly.
"This is a real shame. I would have liked to be part of the team for this game. I hope that my team-mates will record a win nonetheless," Neuer was quoted as saying on the official DFB website.
Low has opted to call-up Borussia Monchengladbach goalkeeper Marc-Andre ter Stegen as the former Schalke man's replacement.
The 20-year-old made his official Germany debut in a friendly against Switzerland ahead of Euro 2012, but initially missed out on a call-up for the match against Argentina as Low preferred Ron-Robert Zieler.
Wednesday's encounter in Frankfurt kicks off at 20:45CET.