TORONTO—Money laundering pushed house prices up roughly 5% in the Canadian province of British Columbia last year, according to government reports, highlighting the influence of a growing tide of dirty money on one of North America’s hottest real-estate markets and Canada’s economy.

Roughly 5 billion Canadian dollars ($3.71 billion) worth of illicit funds flowed through the real-estate market last year, including in Canada’s third-largest city, Vancouver, with another estimated C$2.4 billion moving through the province’s casinos,...