The Armenian playmaker joined the club earlier in July but the 24-year-old picked up a knock during Tuesday's friendly with Luzern in Switzerland.
"Borussia Dortmund have to make do without Henrikh Mkhitaryan in the coming weeks," a club statement read. "According to team doctor Markus Braun he will probably be unavailable for up to four weeks."
The former Shakhtar Donetsk man will miss the DFL-Supercup fixture with Bayern Munich on July 27, the club's first round DFB-Pokal clash a week later and its Bundesliga season opener against Augsburg on August 10.
However, Dortmund hopes he will be available for the first home league game against Eintracht Braunschweig on August 18.