Gotze scored Dortmund's third goal as they raced into 4-0 lead after just 25 minutes of the Bundesliga clash at Signal Iduna Park.
But the Germany international had to be replaced by Gonzalo Castro in the 78th minute as Schalke came roaring back to earn a point away to their bitter local rivals.
Dortmund announced on Twitter that Gotze will be sidelined "due to a ligament tear in the upper and lower right ankle for six weeks".
The 25-year-old suffered calf, knee and adductor problems between August and December 2016, before missing much of the second half of last season with a metabolic illness.
He is now unlikely to return to action until after the mid-season break.