It is not now, but it was until 1982, when they were granted sovereignity. Although they are now a sovereign nation, they are still a monarchy, and the Queen of Canada happens to be the Queen of Britain.

From the website of the Canadian Parliament
Canada is a democracy, a constitutional monarchy. Our head of state is the Queen of Canada, who is also Queen of Britain, Australia and New Zealand, and a host of other countries scattered around the world from the Bahamas and Grenada to Papua New Guinea and Tuvalu. Every act of government is done in the name of the Queen, but the authority for every act flows from the Canadian people.