The player took a Qatar Airways flight with the flight number QU149 at 8:08 local time (6:08 CET) which was set to arrive at 13:33 CET, according to 'L'Equipe'.
The day he returned to training with the whole team, after having problems in his left leg, the player suffered a tear in the quadriceps in the same leg. That will prevent him from playing in his second World Cup after the one in Brazil in 2014.
"I've never given up, but I have to think about the team, as I've always done, so the sensible thing is for me to give up my place to someone else who can help the team and have a great World Cup," Benzema wrote on social media in the early hours of the morning.
The MRI scan he had revealed a tear to his left quadriceps and that requires three weeks rest, according to the statement issued by the French FA (FFF).
Coach Didier Deschamps lamented the absence of the recenty Ballon d'Or winner, who had until Monday, the day before the opener with Australia, to call up a replacement. However, the boss ended up deciding to stick with his 25 men.