Sometimes you will need to get a license in the province where you would be practicing. How that is done is a question the people at the institution where you would train would be best able to answer.
I personally know two people who did fellowships in Canada. One was a Canadian, so for him it was no issue. The other was a citizen of a third country, not Canada or USA, but had a USA green card. I don't know the particulars, but he was obviously able to secure the status necessary for him to do his fellowship. Both were well-known and competitive fellowships and both were competitive candidates.
