The 23-year-old was substituted at half-time of Saturday’s 4-3 defeat at Bayer Leverkusen, which left his team third in the Bundesliga.
Dortmund said Brandt had suffered torn ankle ligaments and will miss Friday’s league clash at home to Eintracht Frankfurt.
They have not said whether the German international will be fit for their Champions League first leg at home to PSG on February 18.
Dortmund are already without captain Marco Reus, who suffered a leg injury in their German Cup loss at Werder Bremen last month.
