Depends on the industry.
One of the reasons why so many internationals end up working in consulting firms and investment banks post-MBA in the US is because of the visa issue, since these two industries are the ones that are most willing to sponsor international MBAs without hesitation. Tech firms are also willing to hire internationals, although this is more biased towards technical positions than MBAs, since by law there is a cap limit on the percentage of US-based employees that need work visas (I don't know the percentage offhand, but I believe it's around 20%, and so tech companies are understandably wanting to use most of that cap for technical positions and not MBAs).
The work visa most Canadians with MBAs would get in the US is the H1 just like any other non-US citizen. Canadians are also eligible for the TN visa which is easier to get (you can get it right at the border with an offer letter), but they are meant to be temporary 1 year visas (which you can technically renew forever, although it's a grey area since it's meant to be "temporary"). The road to a green card is typically through the H1 (employment based), although some will get it through marriage (marrying an US citizen) which is a completely separate issue.
For other industries like CPG or media, it really is a case by case basis.
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