The 56-year-old Chancellor paid an unscheduled visit to the home side's dressing room at Berlin's Olympic Stadium after their 3-0 victory over Turkey in a Euro 2012 qualifier on October 8.
She posed for pictures with Germany's star midfielder Mesut Özil, who has Turkish parents, and chatted to the 22-year-old who has been held up as a symbol of integration, which annoyed the country's senior football figure.
German Football Federation (DFB) president Theo Zwanziger was irritated by the visit, which he said had been exploited by Merkel for political gains.
The chancellor's office would not confirm on Wednesday whether Merkel had apologised, but said she had acted to 'clear the air.'
"The events after the game were certainly not ideal, but in a telephone conversation with the Home Secretary and the Chancellor the day after the game we were able to sort the matter out," Zwanziger told SID, an AFP subsidiary. "The matter is now resolved as the chancellor and I have great trust in each other."
Images of the meeting, where Özil and other player are half-dressed, were reluctantly released to the media by national coach Joachim Löw, but Zwanziger has said integration issues in football should not be exploited by politicians.
This is the first time the chancellor, a keen football fan and supporter of the national side, has been in trouble with team bosses.
Pictures of her celebrating Germany's third place at the 2006 World Cup, hosted here, boosted her popularity.