Hernandez injured his left knee during the passage of play which led to Niclas Fuellkrug scoring the only goal of Wednesday's semi-final first leg tie in Germany. The 28-year-old "will undergo surgery in the coming days", said the French champions in a statement.
The 2018 World Cup winner returned to the pitch for a few moments, before being replaced by Lucas Beraldo.
Hernandez is no stranger to serious injuries. At the 2022 World Cup in Qatar, he ruptured the cruciate ligament in his right knee in France's opening group game against Australia.
His latest setback is a blow to France coach Didier Deschamps who will announce his squad on May 16 for the European championships which get underway in Germany on June 14.
"I have no news on Lucas Hernandez. It doesn't look very positive. But we will wait for the doctors to analyse it," PSG coach Luis Enrique said after Wednesday's match.
