The Armenia international only joined the Bundesliga club earlier this month in a club record €27.5million (£23.6million) deal from Shakhtar Donetsk.
However, the 24-year-old hobbled out of the club's friendly with FC Luzern in Switzerland on Tuesday evening.
The 2013 UEFA Champions League runners-up later confirmed that the playmaker faces an extended spell on the sidelines.
"Henrikh Mkhitaryan has been injured in the pre-season friendly and tests have proved he will be out of action for about four weeks overall," a spokesman told Deutsche Presseagentur.
Mkhitaryan will now miss the DFL-Supercup clash with Bayern Munich on July 21, the DFB-Pokal first round on August 3 and their opening day Bundesliga clash with Augsburg on August 10.