Typically, not if you are going to live in Canada. If you are going to Canada for a vacation and not to stay your current auto insurance policy will likely cover your vehicle while you are in Canada. There are certain exclusions in some policies that restrict travelling to Canada and MExico, but that is not commond. To make certain, check with your insurance company's agent that your current coverages will be enough for Canadian laws.

If you reside in Canada then your California policy will not cover you in Canada.

If your current insurance will cover you temporarily, you should ask your insurance company for a yellow Non-resident Inter-Province Motor Vehicle Liability Insurance Card. This card signifies that your insurance company has agreed to provide coverage of not less than the minimum legal requirement in any Canadian jurisdiction in which you will travel. You will also need to keep your car's registration paperwork with you to show authorities if asked.

If you need an auto insurance quote for US or Canada you can get started here.