Konstantelias impressed in his first German Bundesliga start by scoring Dortmund's second goal in the 2-0 victory, but was helped off the pitch early in the second-half.
Dortmund coach Niko Kovac said after the match the club "feared the worst" and they said on Sunday a follow-up examination showed an injury to his cruciate ligament.
"Giannis Konstantelias has suffered a torn cruciate ligament in his left knee and will be sidelined for several months," the club said on social media.
The 23-year-old Greece international joined Dortmund from PAOK earlier in August for a reported fee of €30 million.
The midfielder arrived despite protests from the Greek club's ultras, who occupied the stadium in the hopes of preventing the move, having stopped a similar sale to Bundesliga side Stuttgart a year earlier.