Citizenship is not a requirement for marriage in Canada, but that's no guarantee your marriage will mean anything legally outside of Canada.
Also, Canada is not like the US, you do not gain citizenship from marrying a Canadian citizen. You can be sponsored by your spouse, which let's you stay in the country, until you become eligible to apply for citizenship (which is like 3-4 years in Canada).
However, none of this matters if your boyfriend is not a Canadian citizen.
There are also provisions in Canadian immigration law that recognize same-sex couples for family reunification if they come from a country where same-sex marriages aren't legal. However, it's complicated and would usually involve showing that there was a long term relationship.
As a permanent resident, your boyfriend will eventually become eligible for citizenship, but who knows how long that will be for him.
http://www.cic.gc.ca/english/newcomers/about-pr.asp
Edit: My recommendation would be to contact a consulate or embassy in the Ukraine, or contact Citizenship and Immigration Canada for information.