Benzema sustained the injury during the Champions League group stage match against Celtic.
Newsonline report that the France striker was forced off after just 30 minutes at Celtic Park on Tuesday as Madrid beat the Scottish Premier League side 3-0.
Madrid said in a statement: “Following tests carried out on our player Karim Benzema by the Real Madrid Medical Services, he has been diagnosed with an injury to the semitendinosus tendon and a strain to the quadricep muscle in his right thigh. His recovery will continue to be assessed.”
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ESPN reports the injury will keep Benzema out for a month, meaning he will miss Los Blancos’ second Champions League group stage match against RB Leipzig.
Benzema, 34, scored 15 goals in 12 matches in the Champions League last season as Carlo Ancelotti’s side lifted the European title.