One of two Canadian soldiers run down by a car driven by a suspected Islamic militant has died, police said, the first such incident in Canada since the country joined the fight against Islamic State militants.

A police spokesman said the soldier died late on Monday. His name, age and rank were not released. The soldier was one of two walking near a Quebec strip mall when they were run down by the car on Monday morning.

Quebec police said the 25-year-old driver was shot and killed after a chase following the incident in Saint-Jean-sur-Richelieu, around 40 km (25 miles) south east of Montreal.

Prime Minister Stephen Harper's office said he was known to federal authorities. There were clear indications he had become "radicalised." The government has used the term to refer to Canadians who supported militant Islamic groups.

Canadian media, citing police sources, identified the driver as Martin Couture-Rouleau, a resident of the Quebec town, and said he had a Facebook page under the name of Ahmad Rouleau. A neighbour said Rouleau became radicalised about a year ago after getting involved with extremist Muslims. He posted a quote from an early Muslim caliph, Umar Ibn Khattab: "I will not calm down until I will put one cheek of a tyrant on the ground and the other under my feet, and for the poor and weak I will put my cheek on the ground."