The suspect was shot by police after a chase in the Quebec city of Saint-Jean-Sur-Richelieu. A second soldier suffered minor injuries in Monday's attack.
Steven Blaney, Canada's public safety minister, said on Tuesday the attack was "clearly linked to terrorist ideology".
Guy Lapointe, Quebec Police spokesman, said the act was deliberate and that one of the two soldiers was in uniform. He said there were no other suspects at this time.
An official who spoke on condition of anonymity because he was not authorised to speak publicly about the case identified the suspect as Martin Couture-Rouleau, 25. The suspect was known to authorities and recently had his passport seized, Royal Canadian Mounted Police Commissioner Bob Paulson said.
He was one of 90 suspected people in the country who intend to join battles abroad or who have returned from overseas.However, it was not known whether the suspect had any ties to armed groups.
"He was part of our investigative efforts to try and identify those people who might commit a criminal act travelling abroad for terrorist purposes," Paulson said.
A Quebec business data base shows Couture-Rouleau started a water-pressure cleaning company in St-Jean-sur-Richelieu in 2012 with two other people.