Fans in the northern Italian city gathered in San Carlo Square to view the match on a big screen. Their beloved local team, Juventus, competed against Real Madrid in the match, in Cardiff, Wales.
But chaos ensued during the outdoor party, sparking the crush.
Italian news agency ANSA is now reporting 1,527 people, three of whom were in serious condition.
"The underlying cause was panic, what unleashed the panic has to be understood," said the prefect of Turin, Renato Saccone, who arrived to Piazza San Carlo to see what had happened.
The prosecutor's office has kicked off a probe into the incident, which occurred in a continent edgy over the threat of terror.
It was not known what caused the stampede.
Monica Viscovo, press officer of the Turin state police, said some eyewitnesses reported an explosion. There was also speculation of a fireworks explosion or a firecracker.
Authorities said people were injured when a railing fell.
Antonio Scarmozzino, director of the Molinette Hospital in Turin, said around 350 people were treated, with three of them badly hurt. Two women and a boy were in serious condition after they were "crushed by the people trying to escape," he said.
"I'm shocked at what happened in San Carlo Square, #Torino, and close to the people involved. We're watching the situation minute by minute," Turin Mayor Chiara Appendino said on Twitter
The square was littered with debris and people who came to watch the match left behind shoes and other belongings.
Real Madrid won the match 4-1. The win was a milestone in the Champions League, a popular yearly competition for the top European teams.
The Spanish team won its 12th European Cup and become the first team in 27 years to retain the trophy.
Real Madrid is the first team to win back-to-back titles since the competition morphed into the Champions League.