Hernandez suffered the injury in the opening minutes of France's 4-1 victory over Australia in their group stage game on Tuesday.
The Bayern Munich left back was taken off and replaced by brother Theo Hernandez.
The news means France have suffered another major injury setback in their quest to retain their world title.
Paul Pogba, N'golo Kante, Presnel Kimpembe, Christopher Nkunku and Karim Benzema were all ruled out before France kicked a ball in Qatar.
Hernandez played a key role as France won the World Cup in Russia four years ago.
"Lucas Hernandez had an MRI at the Aspetar clinic after the match against Australia (4-1). This examination unfortunately confirmed the clinical diagnosis: a rupture of the anterior cruciate ligament of the right knee. Lucas Hernandez is therefore unfortunately forfeited for the rest of the World Cup," a statement read.
France manager Didier Deschamps sent his well-wishes to Hernandez after the announcement, telling fff.fr: "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. 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."
It is likely Hernandez will also miss the rest of the 2022/2023 season when club football resumes after the World Cup.
