Just after 5 p.m. on Thursday, two cars and a pick-up truck collided in the Charlesbourg neighbourhood.
Const. Pierre Poirier of Quebec City police said witnesses reported seeing the driver of the pick-up running from the scene.
When they peeked inside the truck, they found two children, aged two and four. The children were not seriously hurt and have been taken into youth protection custody.
Poirier said investigators are trying to determine the nature of the relationship between the man who ran away and the two children.
A K-9 unit joined the search for the missing driver, who has not yet been tracked down.