The Turin prefect said in a statement that the crowd "was taken by panic and by the psychosis of a terror attack," fearing that a loud noise was caused by attackers.
The source of the loud noise that triggered the stampede remained unclear, officials said. Italian media has speculated it may have been a firecracker.
The noise triggered panic among thousands of fans gathered in Piazza San Carlo to watch the match pitting Juventus against Real Madrid on giant TV screens. Fans were trampled as they tried to flee.