The 26-year-old suffered the injury to his right leg in Sunday's 1-0 win over Borussia Monchengladbach, a result that ended a five-match losing streak for Dortmund in the Bundesliga.
However, the Greece international will miss just a fortnight of action after the club confirmed he will be back for the UEFA Champions League match at Arsenal on November 26.
Sokratis would have been unavailable for the next league match against Paderborn anyway, having picked up his fifth yellow card against Monchengladbach.
Dortmund were helped off the foot of the German top flight by Christoph Kramer's remarkable own goal from inside the centre circle.
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