According to reports from Switzerland, the FC Basel forward was tackled by defender Steve von Bergen in training and had to be treated before limping off at Zurich's Letzigrund stadium.
It remains unclear how serious the injury is and whether it may prevent Frei, one of Switzerland's key players, from participating in the tournament.
30-year-old Frei has 40 scored goals in 73 appearances for his country and unfortunately also missed most of Euro 2008 through injury.
Swiss coach Ottmar Hitzfeld is scheduled to hold a press conference later on Wednesday to reveal the full extent of Frei's problem.
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