The Armenian, who was the subject of a €27.5million move from Shakhtar Donetsk early last week, picked up the problem during Dortmund's 4-1 friendly win over FC Luzern on Tuesday.
He scored his second goal in two pre-season appearances for the German club in that game, but limped from the field after sustaining the blow.
And, after the player underwent a scan on Wednesday, Dortmund have confirmed that their new signing will be sidelined temporarily.
Mkhitaryan became Dortmund's most expensive signing of all time after finalising his move from Ukraine, with the player snubbing interest from Liverpool in order to join the 2012-13 UEFA Champions League finalists.
The 24-year-old rose to prominence last season as he scored a record 25 goals in 29 Ukrainian Premier League appearances to lead his team to the title.
He also helped Shakhtar reach the last 16 of the UEFA Champions League, where they were knocked out by his current club.
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