Insurance companies policy terms differ as do internal guidelines of individual insurance providers but in general damage to your vehicle form the tire falling off or having a blow out would be a comprehensive claim.
Generally when an automobile part, such as a tire, causes an accident or damage to a vehicle a comprehensive policy would cover damages that resulted from the incident but not necessarily the replacement cost of tire.
If you had recently had the tires a tire fall off your vehicle causing damage to the car itself then you should check with your insurance agent to make certain this incident would be covered by your policy.
If it is determined not to be covered under the terms of your physical damage coverages then you may need to determine the reason the tire fell off of your vehicle. By finding out the reason the tire fell off, such as a mechanic forgot to tighten the lug nuts after working on the car at his shop, then you may find that someone else is liable for the damages your automobile sustained.