It depends on the province but usually you send the claim to an insurance company. If you were insured by a personal policy and/or an employer's policy, it could be either of them. If you were completely uninsured, it's the policy of the car that hit you that will pay. In case of a hit and run or if all motorists were uninsured, you might have recourse to a provincial fund. You province's website or Google have information.
You are treated like every other John Q. Public, there is no seperate process for foreign workers.
If you still have no idea what to do, tell us the name of your province, if you had car insurance and if you were a pedestrian, driver or passenger.