The Germany coach says the defender's comments regarding Mannschaft's defence are not a problem, while the player himself insists they have been taken out of context
Hummels allegedly said that he has more trust in his team-mates at BVB than at international level.
"With BVB, I know that one of my fellow defenders is always there to make amends when something goes wrong. I don't have that assurance with the national team," Hummels told German magazine Focus.
Germany boss Low was then quizzed on the defender's comments, but insisted he had no problem with his words providing he continues to do as he is told for the national side.
He said: "What Mats Hummels said isn't problematic. The important thing is that the players do what the coach tells them on the pitch, both at their club and with the national teams. And that's the case with Mats Hummels."
Hummels has been angered by the quotes used from the interview, claiming they have been taken completely out of context and that he would never be so critical of Germany or his national coach.
"I am very disappointed that they [Focus] scrapped a crucial part of what I said," the defender stated. "My comments get a completely different meaning this way. I never criticised Jogi Low's or the national team's playing style."