The Bayern Munich youngster had emerged as one of the most exciting young talents in Germany's squad after impressing throughout the campaign. Karl also made history by becoming Bayern's youngest-ever goalscorer in the UEFA Champions League.
The injury occurred ahead of Germany's final World Cup warm-up match against the United States. Karl was taken for medical scans, and Germany head coach Julian Nagelsmann immediately feared the worst.
Speaking after the diagnosis was confirmed, an emotional Karl shared his disappointment on Instagram.
"I have no idea where to start but it's just indescribably painful being forced to miss the biggest tournament of all," he said.
"I've done everything to be fit for the World Cup. Unfortunately injuries often come at the unluckiest time."
Nagelsmann admitted the loss was a major setback for both the player and the national team.
"I feel incredibly sorry for Lenny," the Germany manager said. "With his light-heartedness, his creativity, his pace and his personality, he fit into the team perfectly."
"It is a huge shock for him and for all of us that he will miss the World Cup. It is only a small consolation that he is young and still has many tournaments ahead of him."
Germany have moved quickly to replace Karl, with midfielder Assan Ouedraogo called into the squad under FIFA regulations that allow teams to replace players suffering serious injuries before the tournament.
Nagelsmann expressed confidence in the newcomer, saying: "With Assan Ouédraogo we are now getting a player who, similar to Lenny, had a great start with us. He is also highly talented and is meant to play here boldly and freely."
Germany will begin their World Cup campaign in Group E, where they are set to face Curacao, Cote d'Ivoire and Ecuador in the group stage.