If you have comprehensive coverage on your vehicle it should be covered for the damage done to your vehicle from hitting the deer. Comprehensive covers losses due to falling objects, fire and colliding with a bird or animal. Collision coverage is what you would use if your car was hit by a run away shopping car since that coverage covers being hit by another vehicle or object.
Typically your deductible for your comprehensive coverage would apply. You can ask and see if your insurance company will waive it. In some states collisions with wildlife is covered by the state or the state asks the insurance company to waive the deductible amount, but I could not find this to be true for Minnesota.
Minnesota's Department of Public Safety does give information what to do if you have hit a deer. Dawn and dusk is the most likely time to have an accident with a deer. If you have hit a deer call 911. The law enforcement officer will come out and determine your damages. Also they can issue a permit if you want to legally transport the deer away from the scene for your own use.