A soldier has been wounded in the attack, Canadian media report.
The incident comes amid the nation's raising of its terror threat level from low to medium, after a Muslim convert was killed by Quebec police after hitting two soldiers with his car.
"Shots fired at War Memorial at 9:52am today; one person injured," Ottawa Police tweeted on Wednesday.
A government official earlier said the raised threat level was in response to an increase in online "general chatter" from radical groups including Islamic State and al-Qaeda.
Ministry spokesman Jean-Christophe de Le Rue said on Tuesday that the increased level "means that intelligence has indicated that an individual or group within Canada or abroad has the intent and capability to commit an act of terrorism".