Goals from Raffael and Max Kruse had put Gladbach 2-0 up at Borussia-Park, but Havard Nordtveit's red card and Milos Jojic's deflected strike gave Dortmund hope of rescuing a point.
Substitute Marvin Ducksch thought he had done just that in the closing stages, but Robert Lewandowski was penalised for a foul in the build-up.
The decision incensed Dortmund coach Klopp, who continued to berate the officials until referee Deniz Aytekin sent him to the stands.
Klopp has already served a two-game touchline ban in this season's UEFA Champions League for his conduct towards officials in September's defeat at Napoli.
And the DFB's disciplinary committee chairman Anton Nachreiner hinted his previous indescretions could count against him as they consider a suitable punishment.
He told Bild: "That Jurgen Klopp is a repeat offender could have an influence on the sports court's ruling."
Dortmund chief executive Hans-Joachim Watzke was quick to back Klopp after the match, claiming: "In this matter, I must come to Klopp’s defence 100 per cent.
"He did not insult anyone. What Klopp has done, 17 other coaches in the league also do."
