If a person holds prejudice against people because of their nationality, would that be considered racist?

Would it be considered racist if a store owner believes all Canadians are thieves and does not let any Canadians into his store? Racism pertains to discriminating based on race, and (correct me if I'm wrong) Canadians are not a race. What would be an appropriate word to describe an individual such as the store owner?

The discrimination is specific to Canadians, not foreigners in general. I'm looking for a word that could be applied to someone who lives in the country they discriminate against. For example if a Canadian announces "all Canadian culture is stupid!" what would that be called?

That's a xenophobe:

one unduly fearful of what is foreign and especially of people of foreign origin.

More generally, and not limited to nationality or origin, is a bigot:

a person who strongly and unfairly dislikes other people, ideas, etc. : a bigoted person; especially : a person who hates or refuses to accept the members of a particular group...

(and that includes Canadians).

The definition of racism is very fuzzy, partly because the definition of race itself is fuzzy, partly because the definition of discrimination is fuzzy, and partly because racism and other kinds of bigotry tend to go hand in hand.

While most conceptualizations of racism include the notion of “race based discrimination,” the exact definition is controversial both because there is little scholarly agreement about the meaning of the concept “race,” and because there is also little agreement about what does and does not constitute discrimination.

Wikipedia goes into some detail on this confusion. This part is particularly relevant to the question at hand (emphasis added):

Among the questions about how to define racism are the question of whether to include forms of discrimination that are unintentional, such as making assumptions about preferences or abilities of others based on racial stereotypes, whether to include symbolic or institutionalized forms of discrimination such as the circulation of ethnic stereotypes through the media, and whether to include the socio-political dynamics of social stratification that sometimes have a racial component. Some definitions of racism also include discriminatory behaviors and beliefs based on cultural, national, ethnic, caste, or religious stereotypes.

So not everyone agrees, but if you wanted to call the scenario in your question racism, you surely wouldn’t be alone.

Technically believing that Canadians are bad is not racist, as Canadians are not a race - and are made up of many races. However the word is used in this situation, since there doesn't seem to be a viable alternative. 'Nationalist' means something else, and 'xenophobe' applies only if the prejudice is directed at all foreigners.