The 29-year-old from Calgary recorded a time of 24 minutes 24.9 seconds, finishing between Norwegian brothers Johannes Thingnes Boe and Tarjei Boe.
"It is just surreal," Smith said. "I had a strong relay earlier in the week so I had good feelings about today, but never expected to do this at all."
Two-time Olympic champion Myriam Bedard is the only other Canadian to reach the podium at a biathlon world championships, claiming a gold and silver in 1993. No Canadian male has reached the podium.
"May of these top guys are regularly on the podium, but I realized over the last little while they are not gods," Smith said. "They are super talented people, but I knew I can be there with them. It is awesome to be on the podium. I definitely felt it was a matter of time, but I didn't expect to do it at world championships."
Thingnes Boe, who won his first world title, missed his 10th and final shot after hitting the first nine at the two shooting stations, but finished in 24 minutes 12.8 seconds. Smith also hit nine of 10 targets, finishing was 12.1 seconds behind. The older Boe brother shot clean but finished 25.3 seconds back.
The other favourites struggled at the shooting range, with Martin Fourcade of France missing three targets to finish 12th.
Smith, along with Canadian teammates Brendan Green and Rosanna Crawford have all broken into the top-five this season, and Chris Lindsay, Biathlon Canada's high performance director, believed it was only a matter of time before one of them reached the medal podium.
"These results are the natural progression in our plan," Lindsay said. "We have depth. Our entire program believes we can be on the podium, and Nathan proved that today."