Quebec provincial police said he died early today. The soldier's name was not released at the request of the family. The other soldier's injuries were described as less serious.
The suspect was shot by police, and later died, after he struck the two members of the Canadian military with his car in a city near Montreal.
An official familiar with the case identified the suspect as Martin Couture Rouleau, 25, of Saint-Jean-sur-Richelieu, Quebec, and said he was influenced by radical Islamists. The official spoke on condition of anonymity because he was not authorised to speak publicly about the case.
One neighbour told reporters that Rouleau stopped wearing jeans and started wearing a tunic and that he had changed over the past year and was alone a lot. Another neighbour said Rouleau converted to Islam a little over a year ago.
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A Quebec business database shows Rouleau started a water-pressure cleaning company in St-Jean-sur-Richelieu in 2012 with two other people.
Police declined to provide details, citing the investigation.
Quebec police shot the man after two Canadian Forces members were struck by the motorist yesterday in a mall parking lot near Montreal. The suspect died a few hours after being shot.
After the man hit the two soldiers, he fled the scene in his vehicle, triggering a police chase that ended with the man losing control and his car rolling over several times.
Brunet said the man exited the car and was shot. Brunet said they found a knife on the ground but he could not say if the suspect had it in his hand when police fired their weapons. Television images showed a large knife in the grass near the flipped-over car.
Canadian Prime Minister Stephen Harper was briefed about the incident by the head of Canada's national police force, the head of the military and his national security adviser.
Harper said in Parliament yesterday that he was aware of the reports and called them "extremely troubling.