Around seven people were seriously hurt, including a seven-year-old boy who was trampled and suffered head and torso injuries.
It is believed a firecracker exploded during the second half of the match, shortly after Real Madrid scored their third goal, causing people to fear the worse.
Video footage showed crowds running from the square towards Via Roma, screaming in fear, as barriers came crashing down and a glass window at Caffè Torino shattered.
“It was like Heysel all over again,” a Juventus fan who was caught up in the carnage said, referring to the Heysel Stadium disaster in 1985 which killed 39 people, including 32 Italians.
Shortly after the stampede unfolded, security forces and fire-fighters tried to calm the crowd as ambulances rushed to the scene.
Police set up information points to help people track down their loved ones, as distraught children and adults limped around in search of friends and family.
By 11:00 pm, Piazza San Carlo was completely empty except for shoes, bags and litter scattered across the ground.
Turin authorities began investigating the incident immediately, checking footage from the area’s security cameras to determine what exactly caused the stampede.