The stampede which followed caused minor injuries to what was initially thought to be around 50 supporters, though Rai TV is reporting 400 injuries.
Juventus' fans run away from San Carlo Square following panic created by the explosion of firecrackers as they was watching the match on a giant screen.
Real defeated Juventus 4-1 to win the Champions League for the 12th time. About five people were seriously hurt, including a seven-year-old boy who was trampled, Sky TG24 reported.More news: Warriors star Stephen Curry a different player this NBA Finals
He said some reported having heard a small explosion, others a shot.
Another witness told Italian paper La Stampa: "We heard screaming and at some point thousands of people began to press to run out of the square".More news: Cops treating London van attack as 'terrorist incident'
An injured Juventus fan cries at the end of the Champions League final in Turin's San Carlo square.
Afterwards shoes and bags littered the ground, while people were seen limping and searching desperately for friends and relatives, according to a witness.
Police are now investigating the cause of the mayhem.More news: Cristiano Ronaldo bags brace as Real Madrid clinch Champions League
The square was evacuated quickly and local official Renato Saccone said: "The root cause of this was panic, to understand what triggered it we will have to wait a while". "There was an incident there; we hope that not too many people were injured".
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