The Slovakian midfielder was introduced as a second-half substitute on Saturday as Napoli suffered a surprise defeat to Parma, but was forced off within 10 minutes after hurting his left foot.
Subsequent scans have shown Hamsik has avoided a fracture.
However, he will miss the trip to Signal Iduna Park, which will see Rafael Benitez's side seek a victory that would guarantee qualification for the knockout stages.
Napoli currently sit second in Group F, level on points with leaders Arsenal and three points clear of Dortmund.
However, the Italian club have suffered back-to-back league defeats either side of the international break, with the reverse against Parma following a 3-0 loss at Juventus.
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