No, normally your Physical Damage coverage (Collision or Comprehensive) deductible would not be waived in this sort of incident. Typically whether you are at-fault or not in an accident your Collision or Comprehensive, is due to your insurer. In the incident you described it would be your Collision coverage deductible that would be due since another vehicle collided with your car and damaged it.

State laws and insurance companies’ rules differ so some may waive a deductible if you are not at fault and/or in the case of a hit and run, which occurred in your situation since the other car did not leave their information after they hit your vehicle.

If you believe that in your state that car insurance deductibles are waived for not at fault accidents or hit and run claims you can try contacting your state's insurance regulator for information on if your deductible is due or not.

Normally a state's insurance regulatory agency has a consumer division that will help consumers with questions regarding auto insurance and claims procedures.