Marí, a 29-year-old Spanish defender, suffered a stab wound to the back - but his injuries are not life-threatening. His agent, Arturo Canales, told the BBC that the star was conscious and no vital organs had been affected.
Monza CEO Adriano Galliani told Sky Italia that Marí had been shopping with his wife and young son when the attack took place.
"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 said.
"Unfortunately, he also saw the criminal stab someone in the throat. He saw everything that happened and it was deeply disturbing," Galliani added.