Yes, starting a business in Canada when you’re nonresident in Canada is possible – but certain requirements have to be met.
First, are you Canadian? If you are, then all you need is a Canadian address (not a Post Office box, but a real Canadian address). Then you can register your new business in the province that it’s located in.
If you personally have or establish a Canadian address and are a Canadian citizen, you can register your business as a sole proprietorship.
Or you could form a partnership with a Canadian living in Canada; then you can use his/her address for starting your business in Canada.
Another approach is to start an incorporated business. You would still need a Canadian address to enjoy the tax benefits of having a Canadian Controlled Private Corporation (see Types of Corporations in Canada and Corporate Tax), as well as have the correct number of Canadians on your Board of Directors and meet all the other requirements for such a corporation.
The correct number of resident Canadians depends on the jurisdiction you incorporate in. In Canada you may incorporate federally or provincially for starters.