He will be replaced in the squad by Kasper Schmeichel, whose father Peter played a key role when Denmark won the European Championship in 1992.
Coach Morten Olsen said he could not afford to bring a goalkeeper carrying an injury to the tournament, where Denmark will face Netherlands, Germany and Portugal in the group stage.
"It's a tough decision I had to make, and it's a serious blow for us sportingly," Olsen said, adding that the uncapped Schmeichel will be adequate backup for Stephan Andersen and Anders Lindegaard.
"He (Schmeichel) has worked very seriously on his development as a goalkeeper, and we have followed him closely during the season at Leicester."
Sorensen was substituted in the first half of the 3-1 defeat by Brazil and was replaced by Andersen who is likely to start in Denmark's Group B opener against Netherlands on June 9.
Olsen, who named a preliminary squad on May 16, gave the final outfield places to Groningen striker Niclas Pedersen and 19-year-old central defender Jores Okore from new Danish champions FC Nordsjaelland.