Investigators have ruled out terrorism, and police have arrested a 46-year-old man.
Mari is on loan at Italian side Monza from Arsenal, who signed him from Brazilian club Flamengo in 2020.
Arsenal manager Mikel Arteta has said Mari “seems to be OK”.
“I know [club technical director] Edu has been in touch with his relatives,” said Arteta after Thursday’s 2-0 defeat at PSV Eindhoven in the Europa League.
“He is in hospital. He seems to be ok. I will get a briefing now about what happened.”
Arsenal issued a club statement on Thursday night: “We are all shocked to hear the dreadful news about the stabbing in Italy, which has put a number of people in hospital including our on-loan centre-back Pablo Mari.
“We have been in contact with Pablo’s agent who has told us he’s in hospital and is not seriously hurt.
“Our thoughts are with Pablo and the other victims of this dreadful incident.”
Monza chief executive Adriano Galliani has told Sky Italy Mari was stabbed in the back and has a “fairly deep wound”, but his injuries are not life-threatening.
Galliani said: “Pablo Mari had a fairly deep wound on his back, which fortunately did not touch vital organs such as the lungs or others.
“His life is not in danger, he should recover quickly.”
Galliani later also told Sky Italy that Mari, who is 6ft 4ins, was “saved” due to his height, and said Mari had his son in the shopping trolley.
“He told me about this incredible incident,” said Galliani. “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.
“Unfortunately, he also saw the criminal stab someone in the throat. He saw everything that happened and it was deeply disturbing.”
Mari is recovering at the Niguarda hospital and told Galliani he wants to be back in training on Monday.
On Twitter Galliani wrote: “Dear Pablo, we are all here close to you and your family, we love you, keep fighting as you know how to do, you are a warrior and you will get well soon.”