According to local media, a man began attacking people in Assago, and a 30-year-old grocery employee was killed as a result.
Pablo Mari, a football player on loan from Arsenal, was one of the hurt.
A suspect, 46, has been taken into custody. Terrorist intent has been ruled out by the police.
According to reports, the attacker had mental health issues and had taken the weapon from the grocery store racks.
Around 18:30 local time (16:30 GMT), the man began randomly stabbing people at a Carrefour in a nearby retail centre.
Inside the center, people were allegedly screaming as they scurried away in fear.
According to reports, several clients stopped the attacker and turned him over to the police when they got on the scene.
Mari, a 29-year-old Spanish defender, was stabbed in the back, but he is not in critical condition. According to his representative, Arturo Canales, the celebrity was aware and his essential organs were unharmed.
According to Adriano Galliani, CEO of Monza, who spoke to Sky Italy, Mari was attacked while out shopping with his wife and little boy.
“He had his son in a trolley and his wife next to him. He didn’t notice anything. He then felt something painful in his back, which was the criminal’s knife,” Mr Galliani added.
“Unfortunately, he also saw the criminal stab, someone, in the throat. He saw everything that happened and it was deeply disturbing,” Mr Galliani stated.
The CEO acknowledged that the player had a “fairly deep wound on his back,” but said that there was no danger to his life and that he “should heal fast.”
In January 2020, Mari moved from Flamengo of Brazil to Arsenal. He has only made 19 appearances for the Gunners, and he is presently out on loan to Serie A team Monza.
Arsenal manager Mikel Arteta claimed: “I just found out. I know Edu [Arsenal technical director] has been in touch with his relatives. He’s in hospital but he seems to be okay.”