I certainly think it would be related to moving a rifle to/from a range, so not totally off-topic.
In general terms the safest answer is to put the sword in the trunk of your car while moving it. Other solutions may involve a hard-sided, non-descriptbag that will hide the outline of the object carried in it and can be slung over your son's shoulder as he walks or bikes to the dojo.
As far as the legality, it is generally accepted that if you may legally posses an object, it is not a crime to transport that object in a vehicle, as long as doing so does not pose a clear danger to others, or cause undue alarm. Obviously, your son should not be waving the sword around walking down the street; that is "brandishing" the weapon, which is either its own charge or cause for arrest on disorderly/deadly conduct. Whether it is legal for your son to wear the sword at his side or on his back in a manner such that he can quickly draw it depends on specific Michigan statutes, and though Michigan is an open carry state, the laws may differ with respect to guns vs blades. Not knowing those statutes, and not being a lawyer, I can't say with any certainty that it's legal, and therefore I would follow one of my two above suggestions depending on how your son gets to practice.