Television footage showed Schmeichel was targeted by a spectator using a green laser as England captain Harry Kane stepped up for a penalty in extra time to give the home side a 2-1 win in Wednesday's match at Wembley.
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UEFA had opened disciplinary proceedings against England on Thursday. The FA were also charged following disturbance during the national anthems and for the setting off of fireworks.
Fans booed when Denmark's national anthem was played before kickoff. Jeers were also heard when the German anthem was played at Wembley last week, when England beat Joachim Loew's side in the round of 16.
England are looking to win their first major trophy since the 1966 World Cup and play Italy in the European Championship final at Wembley on Sunday.