Wagner, 30, was not included in Löw's initial 27-man squad and angrily announced his retirement from the national team, telling tabloid newspaper Bild: "It's clear that my open, honest nature doesn't fit with the coaching staff."
But the suggestion that Löw only selects obedient yes-men for international duty has struck a nerve with the usually calm and collected World Cup-winning coach.
"He's portraying some of our most experienced players, leaders in the squad, as complete idiots," Löw said at an event in Berlin hosted by the newspaper.
"As if they're only in the squad because they don't voice their opinions? What should the likes of Mats Hummels or Jerome Boateng think of that? It's ridiculous."
Wagner, who joined Bayern from Hoffenheim in January and who scored 12 Bundesliga goals last season, was excluded from the squad in favor of fellow strikers Timo Werner (RB Leipzig), Mario Gomez (VfB Stuttgart) and Nils Petersen (SC Freiburg), and allegedly cried during training following the announcement.
"Of course I understand that he's disappointed but I think his reaction is over-the-top," continued Löw. "Everyone who works with us knows that we always encourage the players to speak their minds, to be open and honest, and to be critical. We place great value on that."
Wagner has found little support from his club either.
"I was a little bit surprised," Bayern president Uli Hoeness told broadcaster Sky. "There was no need for him to react so angrily."
"I think he reacted too quickly and too emotionally," said head coach Jupp Heynckes, adding that Wagner has otherwise integrated well in Munich. "He's completely focused and very ambitious and always the first player to arrive at training."
Wagner and Löw could come face to face at the German Cup final on Saturday when Bayern Munich face Eintracht Frankfurt. Löw will be in the stands at the Olympic Stadium while Wagner hopes to be on the pitch.