The 34-year-old Real Madrid forward had been struggling with injury for a long time and played less than half an hour of football in his club’s last six games before the World Cup.
On Saturday, he took part in full training for the first time since the World Cup champions met ahead of the tournament last week.
He was forced to withdraw from the session at the home stadium of champions Al Sadd Qatar with the injury and was taken to the trials.
The French Football Federation later said in a statement that the injury “will require a three-week recovery period”, ruling out the possibility of him being fully fit for the tournament, which ends on December 18.
“I am very sad for Karim, for whom this World Cup was the main goal,” France coach Didier Deschamps said in the FFF statement.
“Despite this new blow from the French national team, I have full faith in my team. We will do everything we can to face the huge challenge that awaits us.”
Olivier Giroud, 36, will benefit from Benzema’s absence by joining Kylian Mbappe and Antoine Griezmann in France’s attack.
However, under FIFA rules, Deschamps can still call up a substitute for an injured player until Monday, the day before his first game.
France begin their defense of the trophy against Australia at Al Wakrah on Tuesday.
Denmark and Tunisia will also play in Group D as they aim to become the first team to retain the World Cup since Brazil in 1962.