Schmeichel saved the penalty, but Kane pounced on the the rebound and his goal proved decisive in a 2-1 win which ensured England's passage to Sunday's final against Italy.
European football's governing body said it had opened disciplinary proceedings and has charged England with the use of a "laser pointer by its supporters."
UEFA said its disciplinary investigation will also look at "disturbance" caused by England supporters during the national anthem and the lighting of fireworks by its fans.
Broadcaster ITV, which televised the match in the UK, showed footage of a green laser being pointed at Schmeichel's face.
`"Whoever they are they're an idiot ... it's stupid and he doesn't deserve that," ITV presenter Mark Pougatch said. "That sort of thing, nobody wants to see."
After the incident, the English Football Association's on-site team worked with UEFA to try and find who had used the laser device.
"The Danish FA representative confirmed to the UEFA Match Manager that they did not wish to take the matter any further," according to the English FA.
The Danish Football Union did not immediately respond to
CNN Sport's request for comment.
The disciplinary case will be dealt with by the UEFA Control, Ethics and Disciplinary Body.
Schmeichel had an impressive game for Denmark, notably saving a Harry Maguire header.
