The 22-year-old Turkey star injured his right knee in his side's 3-0 win against Freiburg on Saturday and Dortmund said that a subsequent scan on Monday revealed damage to his ligaments that will sideline him for six weeks.
Dortmund are currently eight points clear of second-placed Bayer Leverkusen in the German top flight with only four matches remaining.
They will be crowned champions on Saturday if they win at bottom club Borussia Moenchengladbach and Leverkusen fail to beat eighth-placed Hoffenheim.
Sahin left the field in the 28th minute of Saturday's meeting with Freiburg.
It may have been his last match for his formative club, as he has been strongly linked with a move to Real Madrid in recent weeks.