The incident—which Prime Minister Justin Trudeau called a "tragic and senseless attack"—was one of the most violent in recent Canadian history.
Toronto Police Chief Mark Saunders identified the suspect as Alek Minassian, 25, who he said had not previously been known to authorities.
The Canadian Broadcasting Corp, citing government officials, said Minassian was not associated with any organised militant group.
Federal Public Safety Minister Ralph Goodale, standing next to Saunders, said: "There would appear to be no national security connections."
The driver steered his vehicle toward people just before 1:30pm. A Reuters witness saw at least two tarp-covered bodies at the site of the incident.
Ryder System Inc spokeswoman Claudia Panfil confirmed that one of the company's rental vehicles had been involved and said the company was cooperating with authorities.
There has been a string of deadly vehicle attacks in the United States and Europe, including an Oct 31 attack in New York that killed eight. The Islamic State militant group encourages its supporters to use vehicles for attacks.
'TRAGIC AND SENSELESS ATTACK'
"It was with great sadness that I heard about the tragic and senseless attack that took place in Toronto this afternoon," Trudeau said in a statement. "We should all feel safe walking in our cities and communities."
Last month, a former Canadian university student pleaded guilty to killing six men praying in a Quebec City mosque in January 2017.
In September, a Somali refugee was charged with attempted murder over allegations he ran down four pedestrians with a car and stabbed a police officer outside a sports stadium in Edmonton, Alberta.
Monday's incident occurred about 30 km (18 miles) from the site where Toronto is hosting a meeting of Group of Seven foreign ministers from Canada, the United States, Britain, France, Germany, Italy and Japan, but had no noticeable effect on that event's security.
"This person was intentionally doing this, he was killing everybody," the man said. "He kept going, he kept going. People were getting hit, one after another."
He said a number of the victims were older people and that he saw at one point a stroller fly into the air.
At least one person was struck outside an Anglican church, north of where the van came to rest in front of a condominium tower.
Some of the victims were struck in a public square popular with office workers on lunch breaks. Aerial photos of the scene posted on social media showed a food truck parked just a few feet away from where emergency workers transferred people onto stretchers.