The full-back sustained a lateral collateral ligament injury to his right knee during his country's 4-2 2018 World Cup qualification victory over Montenegro on Sunday.
Piszczek has been an ever-present for BVB so far this season, playing a key role as Peter Bosz' side have opened up a five-point lead at the top of the Bundesliga.
However, Dortmund have now confirmed the 32-year-old will be "unavailable for the time being" although they have not given any indication of exactly how long the Pole will be sidelined.
BVB face a crucial Bundesliga clash with last season's runners-up RB Leipzig at Signal Iduna Park on Saturday.
Piszczek is also unlikely to be fit for upcoming league games against Eintracht Frankfurt and Hannover as well as next week's Champions League clash with APOEL Nicosia in Cyprus.