Bayern Munich s German head coach Julian Nagelsmann. AFP
The 50,000 euro ($53,200) fine, handed down by the German FA (DFB), means Nagelsmann is free to take his place on the touchline for the top-of-the-table home clash with Union Berlin on Sunday.
According to the DFB, Nagelsmann has already agreed to the fine.
The DFB opened an investigation Sunday after Nagelsmann stormed into the referee dressing room in Gladbach after the full-time whistle on Saturday.
Aggrieved by a contentious red card decision against Dayot Upamecano -- which reduced Bayern to ten men early in the game -- Nagelsmann reportedly used heated language as he confronted referee Tobias Welz.
Journalists outside heard Nagelsmann say "that's a joke, they're taking the piss", before leaving the room calling the officials "spineless".
The Bayern boss later apologised and admitted he had "gone too far", but still insisted the red card was unfair.
Welz defended his decision on Germany's Sport1 network on Sunday morning, and said there was no bad blood between him and Nagelsmann.
"It was an emotional discussion, but there were no insults traded," he said.
Bayern and Union sit alongside Dortmund on top of the Bundesliga table on 43 points, with the Bavarians ahead on goal difference.
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