The patient, identified as Erika, a 38-year-old local woman who had come to watch the match with her boyfriend, was among more than 1,500 people injured in the panic.
There were around 30,000 people in San Carlo square at the time, who had gathered to watch home favourites Juventus play Real Madrid in the Welsh city of Cardiff.
The stampede was apparently triggered by fireworks which were detonated as the match drew to a close.
Two other people were seriously injured, including a seven-year-old boy, who was also left in a coma but is now recovering.
Some of the injuries occurred after a railing around the entrance to an underground car park beneath the square gave way, causing some of those injured to fall up to two metres (nearly seven feet).
Erika was crushed against a wall, and the compression of her rib cage caused a heart attack that led to brain damage, the media reported.
The mayor of Turin, Chiara Appendino, said in a tweet that "words were insufficient" to describe the death, and that the city would officially observe mourning on the day of her funeral.
Ogni parola è superflua. A nome mio e della Città esprimo le mie condoglianze per la morte di Erika.- Chiara Appendino (@c_appendino) June 15, 2017
Sarà proclamato il lutto cittadino pic.twitter.com/NT6seZW6J4
All words are insufficient. On behalf of myself and the city, I express my condolences for the death of Erika. A day of mourning will be announced.
The Italian authorities opened an investigation for involuntary bodily harm immediately after the incident, which will now be upgraded to involuntary homicide.
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Photo: Marco Bertorello/AFP