The Borussia Dortmund striker suffered the injury in the opening Group A match last Saturday, a 1-0 defeat by the Czech Republic.
"He is doing OK (but) we have detected a certain instability" regarding the knee," Wetzel said. "We have spoken to his club doctors and undertaken further tests with a knee specialist in Germany. There are several possibilities. It will probably be necessary to carry out a little surgery."
Frei's loss has been compounded by form and fitness problems with his regular strike partner, Marco Streller, who Wetzel said also potentially faced surgery for a suspected hernia.
The Swiss bowed out of the EUROs after they went down 2-1 to Turkey on Wednesday in Basel.