The Newcastle United defender was knocked unconscious during Saturday's 2-0 win over Georgia.
Schar, however, was cleared to play on in Tiblisi, where he was involved in both goals.
Brain injury charity Headway has called for a UEFA investigation into the incident. In a statement,it claimed the careers, lives and long-term health were being put at "risk" by the sport's "inability to follow its own protocols".
Chief executive Peter McCabe added: "What is it going to take to make football take concussion seriously?"
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Schar, suspended for Newcastle's April 1 game against Arsenal, today left the club's training camp, though he will stay in Switzerland and watch the game in Basel before returning to Tyneside.
Switzerland team doctor Damian Meli said: "Returning after such a collision takes some time. It usually takes a few days, a time that is missing between the two games against Georgia and Denmark."
Speaking after the game, Schar said: "I cannot remember anything. I was knocked out for a few seconds. My skull is still buzzing. I also have neck pain and a bump on the forehead, but it was worth it."