Sorensen suffered a back injury during training and that has now ended his European Championship dreams.
Schmeichel has now been drafted in as the third keeper behind Stephan Andersen and Anders Lindegaard.
"Thomas has suffered an injury in his back," said Morten Olsen.
"It means unfortunately that it is unlikely that he will recover in time to be available for matches for the finals."
Sorensen was hugely disappointed to miss out, saying: "I am deeply unhappy about it. I've been with the team for most of qualifying, and had looked forward to my fifth finals with the national team.
"But I also understand that it is a big risk to go with an injured goalkeeper and therefore I respect Morten's decision, even if it hurts."
Olsen insists he had no qualms about calling up uncapped Schmeichel, saying: "He has worked seriously on his development as a goalkeeper, and we followed him closely during the season for Leicester."
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