The versatile 32-year-old has featured regularly at full-back in recent weeks but an injury in training will see him miss this weekend's clash against leaders Bayern Munich.
Kirch - who has featured six times in the Bundesliga this term - will also likely miss out on Dortmund's DFB-Pokal quarter-final against Hoffenheim.
It represents the latest in a long line of injuries Jurgen Klopp has had to deal with this term, with his side 10th in the top flight following a difficult season.
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