Just for the record if anyone else stumbles upon this:
As a Resident Alien for tax purposes (you can determine your status by following those rules), you are obliged to file your worldwide income in US. Therefore, if you received payments, salary, bank interests, sold stocks, received fellowships etc. anywhere in the world, you have to report them to the IRS. In the specific case of a fellowship, if it is used to pay tuition, books, equipment or anything school related (with few exceptions like housing and travel), you don't have to declare it. Thus, if you're using the fellowship to finance your undergraduate or graduate studies, you don't have to declare it. However, if you're a postdoctoral researcher, you will have to declare it as income since you don't pay tuition and won't be received a diploma after your postdoc.
Once you file your taxes in US, then you file in Canada. Normally, you won't be taxed twice since you already paid taxes in the US.
Hope that helps people :)