Bayern were beaten 3-2 last Saturday at Signal Iduna Park, despite twice leading through goals scored by former Dortmund striker Robert Lewandowski.
Reports emerged after the game that Ribery had "pushed" and "slapped" journalist Patrick Guillou, who highlighted errors by the former France winger in his appearance on beIN SPORTS.
Bayern’s sporting director Hasan Salihamidzic confirmed an incident occurred, and Ribery has now issued a public apology after meeting Guillou.
"I've had an appointment with Patrick Guillou and it was good that he came to Munich," Ribery said in a video posted on Bayern's official website.
"We talked together for a long time and about what happened after the match in Dortmund.
"Of course, what I did was wrong. After the match, I was very emotional.
"I said 'sorry' to Patrick and his family yesterday. And I hope that we can leave this behind – that's why this meeting was important for him and for me."
Bayern are seven points behind Bundesliga leaders Dortmund following their Klassiker loss, which was sealed by a Paco Alcacer strike.
The defeat increased the pressure on under-fire coach Niko Kovac, who replaced Jupp Heynckes for the 2018-19 season and came under scrutiny in October after a run of four games without a win.