Van Koeverden, the face of the summer Games for Canada and the favourite for the title, powered off the start but faded in the final 300 metres. He had been seeking to make amends for his performance in Beijing when he finished eighth despite starting as the favourite.
Van Koeverden took the silver on Dorney Lake to add to the gold, silver and bronze medals he held from previous Games. Germany's Max Hoff came in third for the bronze.
"I will take positives from getting silver," Van Koeverden said, after briefly breaking away from reporters to hug his mother. "(But) if you think you're better than someone else because you beat them by 0.6 seconds, you're not. You're just luckier."
Defending champion Tim Brabants of Great Britain finished last after an injury-plagued build-up to the Games.