It didn't happen in Canada, unless you mean the part where we rounded up all the natives and put them on reserves. I'm a white Canadian born and raised in Canada and I am far from being a minority no matter where I go, from the prairies to the GTA. Conservatives keep talking about this like it's a thing, but they do so from their majority white communities. The only places you see large numbers of immigrants is in low paying service jobs and you can thank the exploitive hiring practices of major companies like Tim Hortons - the people there are slaves living under the constant threat of deportation if they disappoint their employer/owner.

It's also worth noting that those white people concerned about becoming ethnic minorities are themselves immigrants. British and French colonists; German, Ukrainian, Hungarian, Irish; Hutterite and Mennonite - all immigrants, many within just the last few generations. For as long as Canada has been a country, it has been made up of many groups of different ethnicities, all immigrants. "White" isn't an ethnicity.