Benzema was named the 2022 Ballon d'Or winner after helping Real Madrid win the UEFA Champions League and the Spanish La Liga.
"I am deeply saddened for Karim, who made this World Cup a major goal," head coach Didier Deschamps said.
"I never give up in my life, but tonight I have to think about the team as I always do," Benzema said.
"So the reason tells me to give up my spot to someone who can help our team have a great World Cup," Benzema explained.
The French Football Federation stated, "The entire team shares Karim's sadness and wishes him a speedy recovery."
An MRI (Magnetic resonance imaging) scan confirmed the injury, which requires "a three-week recovery period," according to the statement.
On Sunday, November 20, Deschamps told French television network TF1 that he would not name a replacement for Benzema.
In Group D of the ongoing Qatar 2022 FIFA World Cup, France will face Australia on November 22, Denmark on November 26, and Tunisia on November 30.
The 2018 World Cup champions have lost several key players due to injury, including midfielders Paul Pogba, the Juventus star boy, and N'Golo Kante, the Chelsea star boy, who were not included in the final 26-man squad.
Presnel Kimpembe withdrew on Monday after failing to recover from a hamstring injury; he was replaced by Axel Disasi; and forward Christopher Nkunku was ruled out on Wednesday after limping out of training. Randal Kolo Muani was called up to fill in.
Raphael Varane, Manchester United's defender, is hoping to be fit after missing the previous five games.
As of now, Manchester United forward Anthony Martial is a possible replacement for Benzema, who has been out with a thigh injury since October and has played less than 30 minutes in United's last six games.
Saturday was his first full training session since joining the World Cup squad last week.
"Despite this new setback, I have complete confidence in my group," Deschamps said. We will do everything possible to meet the enormous challenge that awaits us."
The World Cup tournament this year will be missing the World Best Player and the Second Best Player - the 2022 Ballon d'Or winners, Karim Benzema and Senegalese star Sadio Mane, respectively.
Credit: The BBC
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