The Bayern Munich defender was forced off in the first half of Tuesday's 4-1 win over Australia and subsequent scans have shown a rupture of the anterior cruciate ligament of his right knee.
It means Hernandez will be set for a lengthy spell on the sidelines and play no further part in the holders' attempts to defend their World Cup title in Qatar.
National team boss Didier Deschamps said: "Like the whole group, players and staff, I am extremely sorry for Lucas.
"We are losing an important element. Lucas is a warrior and I have no doubt that he will do everything possible to return to the game.
"First plan, I know him well. Courage, he will have it, that's for sure.
"On behalf of the group, I wish him the best possible recovery."
Hernandez has become the third player to leave the France camp since the squad linked up for the tournament with Karim Benzema and Christopher Nkunku also suffering injuries during the past week.
Deschamps was already without N'Golo Kante, Presnel Kimpembe and Paul Pogba but still saw France begin their World Cup defence with an emphatic Group D success against Australia.