Low has indicated he will not select Thomas Muller, 30, Mats Hummels, 29, and Jerome Boateng, 30 - who have 246 caps between them - for future games, summarily retiring the trio.
The decision comes with the national team boss ready to move on to a new generation, saying: “This is the year for our new beginning.”
But the timing of it - ahead of key Bundesliga and Champions League games - and finality of the treatment of the three 2014 World Cup winners on a surprise visit to the training ground, has annoyed their club.
In a statement, Bayern said: "National coach Joachim Low has decided not to consider our players Thomas Muller, Mats Hummels and Jerome Boateng in the future.
"Basically, we do not comment on sporting decisions of the national coach, the nomination of the squad of the national team is solely the responsibility of Joachim Low.
"However, we believe the timing and circumstances of the announcement of this decision to the players and to the public is questionable. The last international match of the German national team took place on 19 November 2018.
"The fact that the players and the public were informed three months later, just ahead of important matches for FC Bayern next Saturday in the fight for the Bundesliga title against VfL Wolfsburg and a few days before the decisive second leg in the round of 16 of the Champions League next Wednesday against Liverpool, irritates us.
"In addition, we were surprised that this was done yesterday in the context of an unannounced visit by Joachim Low and Oliver Bierhoff (Director National Teams and Academy) at Bayern.
"Muller (100 caps), Hummels (70) and Boateng (76) have completed 246 internationals for the German national team, they have had an extremely successful decade of the DFB crowned by winning the world title in 2014 as an absolute highlight.
"FC Bayern have great respect for the athletic merits of Thomas, Mats and Jerome for the national team and German football."
Low said: “It was important for me that I could personally tell the players and the bosses at Bayern about my thoughts and plans.”
And he thanked the trio for “many successful and outstanding years together”.
Germany play Serbia in a friendly on March 20.