The 23-year-old midfielder suffered the injury during Dortmund's 2-0 Bundesliga victory over Hamburg on Saturday.
Konstantelias had made an impressive start to his first Bundesliga match for the club and scored Dortmund's second goal before being forced off early in the second half. He needed assistance as he left the pitch, with head coach Niko Kovac admitting after the game that the club feared the worst.
Those fears were confirmed following further medical examinations.
"Giannis Konstantelias has suffered a torn cruciate ligament in his left knee and will be sidelined for several months," Dortmund said in a statement on social media.
The Greece international only joined Dortmund from PAOK earlier this month in a deal reportedly worth 30 million euros, and his injury comes as a significant setback after such a promising start to his Bundesliga career.
His departure from PAOK had been surrounded by controversy, with supporters of the Greek club protesting against the transfer. PAOK ultras had previously intervened in an attempt to stop a proposed move to Bundesliga side Stuttgart.
Dortmund must now continue without their new signing as they prepare for their next match against Hamburg-Eimsbutteler Ballspiel-Club in the first round of the DFB-Pokal on Tuesday at Professor-Reinmuller-Platz.
