Footage has emerged showing the suspect shouting at police "kill me" and "I've got a gun in my pocket" at the scene.
At a news conference on Monday night, Toronto Police Chief Mark Saunders said the act "definitely looked deliberate" but said there is not yet a national security connection.
"We are looking very strongly to what the exact motivation was for this particular incident to take place," Mr Saunders said.
Mr Minassian is from the Toronto suburb of Richmond Hill and was not known to police before the incident.
Canadian outlet CBC cited a profile on social networking site LinkedIn, which identifies Mr Minassian as a student at Seneca College in North York, the Toronto neighbourhood where the attack took place.
The outlet spoke with Ari Bluff, who reportedly went to secondary school with Mr Minassian in Toronto.
"I'm not sure if he had any very, very close friends, at least publicly," Mr Bluff said.
"I never saw him with a group of friends, generally. But whenever we would see him in the hallways, we'd always speak to him or say hi to him or whatnot."
CBC also referred to a Facebook post associated with the same name and the same photo as the one that appears on Mr Minassian's LinkedIn, which "has not been able to independently verify".
Source: CBC via Ari Bluff
The post referred to the "Supreme Gentleman Elliot Rodger." Mr Rodger was the 22-year-old responsible for a deadly rampage in California that left six people dead and a dozen more injured in 2014.
Officers were called to the scene around 1:30 pm (1730 GMT), police said.
A white rental van with a dented front bumper was stopped on the sidewalk of a major intersection, surrounded by police vehicles.
"He was going really fast," witness Alex Shaker told CTV television.
"All I could see was just people one by one getting knocked out, knocked out, one by one," Shaker said. "There are so many people lying down on the streets."
Another witness, Jamie Eopni, told local Toronto television station CP24: "It was crashing into everything. It destroyed a bench. If anybody was on that street, they would have been hit on the sidewalk."
The suspect and a police officer faced off. As the suspect shouted "kill me," the officer replied, "no, get down." When the suspect said, "I have a gun in my pocket," the officer responded: "I don’t care. Get down."
The following arrest was praised as a welcome example of police restraint in the midst of chaos.
Readers seeking support and information about suicide prevention can contact Lifeline on 13 11 14, Suicide Call Back Service on 1300 659 467 and Kids Helpline on 1800 55 1800 (for young people aged five to 25).
Additional reporting: AFP