Benzema teared a muscle in his left thigh during training on Saturday.
An MRI scan later confirmed a rectus femoris tendon injury, which means the 34-year-old will be out of commission for three weeks.
In an Instagram post, Benzema confirmed his departure.
“I’ve never given up in my life but tonight I have to think of the team, as I have always done,” he said. “So reason tells me to give my place to someone who can help our squad have a great World Cup. Thanks for all your messages of support.”
The reigning Ballon d’Or winner will miss the World Cup for the first time since 1978, with the injury occurring three days before France’s World Cup opener against Australia.
France head coach Didier Deschamps said: “I am extremely sad for Karim who made this World Cup a major goal. Despite this new blow for the French team, I have full confidence in my group. We will do everything to meet the huge challenge that awaits us.”
The World Cup champions are already missing Paul Pogba and N’Golo Kanté as they prepare to defend their title against Australia on Tuesday.
Deschamps has until Monday to call up a replacement for Benzema, with Wissam Ben Yedder of Monaco one option.
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