Related question: Those of you who are not American, does your country have a rule that your leader must be a natural born citizen?
No, and for very good reason: Canadian Confederation occurred in 1867, but the status of 'Canadian citizen' did not exist until 1910. Before then, we were merely British subjects, and although there may have been a requirement that our leaders be such, the term was so broad, covering at times over a fifth of the world population, that it was hardly a stringent requirement.
Our head of state is the Queen, who is to the best of my knowledge not a citizen and never has been. Her viceroy, the Governor General, has historically also generally not been a citizen at all, and certainly few were born such. Of our Governors General since 1867, all were British or Irish peers until 1952; of those 17 peers, one each was born in Ireland, India, Italy, and Scotland, and thirteen were born in England. Of the 11 Governors General since 1952, one was born in Hong Kong, and our most-recent foreign-born vicereine, Michaëlle Jean, was born in Haiti, and served as Governor General until 2010. Only 8 of 28 Canadian Governors General were born in Canada.
More of our Prime Ministers, as heads of government, were born in Canada or one of its predecessor colonies, but such was certainly not universal: 4 of our 23 premiers were foreign-born. Our first Prime Minister, Sir John A. Macdonald, was born in Scotland, as was his successor. Our fifth Prime Minister was born in England, as was the much more recent John Turner, our seventeenth Prime Minister, who governed Canada for 79 days in 1984.