Ballack had come in for a storm of protest after he complained to a newspaper about a lack of respect from Löw, with some demanding he resign as captain or even be suspended from the German national team.
“I knew that I would receive criticism for my comments in the press, but I didn't expect it to be this big," Ballack said in a statement.
"Therefore I have to admit that it was a mistake to have chosen this path. I will sit down with Joachim Löw as soon as my health permits and will apologise for my conduct. Because one thing is clear, I'm only interested in the success of the team.”
Ballack had given an interview earlier in the week with the Frankfurter Allgemeine Zeitung in which he demanded more honesty and respect for the national players.
Löw has made it clear the future role of Ballack in the national team will depend on the outcome of the conversation.
"I have registered the explanation of Michael Ballack," he said on the German Football Federation (DFB) website.
"The personal discussion is much more important. Afterwards, I will give a concluding statement."
Bild newspaper reported that Ballack called Löw Saturday to explain the comments, saying he had not meant to criticise him directly but merely protect and support other players who were in a difficult situation.
"I value Jogi Löw personally as a person and as a trainer," Ballack said.
Löw's lawyer said his client had been deeply hurt by the skipper's comments.
"At first, he was completely speechless and disappointed with his captain's comments," Christoph Schickhardt told the Stuttgarter Zeitung newspaper.
"In particular, the comment that he had shown a lack of respect injured him deeply. That was what really annoyed him, it is one of the things he cares about most."
Ballack, who plays for the Chelsea London football club, is currently recovering from a foot operation. He said he plans to travel to Germany to speak personally with the coach and heal the rift as soon as his health allows.