Subotic was injured in a challenge with Ivica Olic and according to the German club's doctor he will be sidelined for at least six months.
The 25-year-old told the Dortmund website: "No worries, I will come back stronger."
Last season's Champions League runners-up lost the match to slip four points adrift of leaders Bayern Munich.
Coach Jurgen Klopp said: "It was a day to forget. In all the tight situations, things somehow always managed to go against us."
Their next game, following the international break, will be against their biggest rivals Bayern Munich.