“It’s a knock on the knee, which also affects the muscle. He felt he was getting stiff so he asked to be subbed,” coach Didier Deschamps told TF1.
“The medical staff are taking care of him.”
Benzema has been recalled to Deschamps’ squad for the tournament for the first time in five-and-a-half years.
He made his first international appearances since October 2015 in last week’s 3-0 friendly triumph over Wales, starting up front alongside Kylian Mbappe, and did so again against Bulgaria before his 83rd France cap was cut short.
France are in the European Championships’ so-called Group of Death, alongside Germany, Portugal and Hungary.
The world champions begin their campaign against Germany in Munich next Tuesday in what looks one of the group stage’s biggest clashes.