The Minnesota Driver's Manual states that owners of motor vehicles must carry no-fault and liability insurance on their vehicles. Valid proof of insurance must be carried in the vehicle at all times.
Typically, a Minnesota auto insurance policy will cover any relative living in your home who does not have a policy of his or her own and they are listed on the policy. This includes spouse and child (who should be listed on your policy).
A driver using your car with your permission and is not covered by another car insurance policy, may also be covered by your policy. This is according to the MN Department of Commerce auto insurance guide.
Minnesota Statutes (169.791) for producing proof of insurance say that every driver should have in their possession at all times when operating a vehicle. If a driver does not produce insurance, they are guilty of a misdemeanor.
The statute goes on to say that if the driver is not the owner of the vehicle, the driver will need to provide proof of insurance on the vehicle by the owner or the name and address of the owner.
From all of this information it would appear that it is the vehicle that must be insured. To make sure that friends and others that you allow to drive your car are covered by your specific car insurance company, check with your agent.