Public Safety Minister Ralph Goodale wrote on Twitter that "there appears to be NO National Security connection to the horrible event" in Canada’s biggest city.
Police identified the driver as Alex Minassian, 25, from the city’s north.
Officers were called to the scene -- on Yonge Street at the corner with Finch Avenue -- at 1:27 pm (1727 GMT), police said, without specifying whether or not the incident was deliberate.
A white rental van with a dented front bumper was stopped on the sidewalk of a major intersection, surrounded by police vehicles.
"Our hearts go to anyone affected," Prime Minister Justin Trudeau told the House of Commons.
"We are going to have more to learn and more to say in the coming hours," he said.
’Really fast’
The incident occurred as Toronto was hosting a meeting of public security ministers from the G7 leading industrialised nations, and on the heels of a weekend gathering in the city for the foreign ministers from the same seven countries -- the United States, Japan, Britain, Germany, France, Italy and Canada.
Vehicle attacks have been carried out to deadly effect by extremists in a number of capitals and major cities, including London, Paris, Berlin, Stockholm, New York, Nice and Barcelona.
Toronto’s police had not stated what they believe the driver’s motives may have been in Monday’s incident.
"He was going really fast," one 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."
And in Quebec in October 2014, a Canadian man ran over two soldiers in a parking lot with his car, killing one of them. The driver was shot dead by police when he attacked them with a knife.
And in March 2016, a Canadian who claimed to have radical Islamist sympathies attacked two soldiers at a military recruitment center in Toronto.
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