The Italian had raised his middle finger after leaving the pitch at the end of the game and later said he had done it because he had been spat on by the home fans.
Bayern scored in the sixth minute of stoppage time with hosts Hertha left fuming over the length of added time that was played.
The DFB said it had ended an investigation into the incident in return for the charity payment.
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"The investigation has ceased in agreement with the DFB sports court. Linked to that is that the coach of Bayern Munich pays 5,000 euros to the Sepp-Herberger charity."
The DFB charity is named after the late Germany coach and works on several social projects.
(Reporting by Karolos Grohmann; Editing by Tom Heneghan)
