The Armenian, who came on in the second half after initially being rested by coach Jürgen Klopp, fractured a bone in his foot in the 90th minute of Saturday's defeat.
Growing injury list
Borussia club doctor Markus Braun gave the diagnosis on Saturday evening after the 25-year-old complained of pain and discomfort as the squad returned to Dortmund after the game.
The news comes as a bitter blow for had coach Jürgen Klopp, who has already lost without Marco Reus, Jakub Blaszczykowski, Ilkay Gündogan, Nuri Sahin and Oliver Kirch to injuries this season. Mkhitaryan is set to miss Matchday 6's Revierderby with local rivals FC Schalke 04, as well as the UEFA Champions League trip to RSC Anderlecht.
Get yourself in the mood for Schalke-Dortmund, the 'mother of all derbies', courtesy of the official Bundesliga YouTube channel: