Since Urgent Care Clinics are cheaper than the emergency room then most times Medicare will not cover the cost of your urgent care visit.
However sometimes Medicare might cover the cost of your urgent care clinic visit if the visit to the urgent care clinic was because of a serious enough injury or illness that could be life threatening.
However most people who do have a severe enough illness or injury would and should go to the emergency room anyway and then Medicare will cover the cost of the emergency room visit.
If the injury or illness was not serious enough then Medicare Part A will not cover the cost of your visit to the urgent care clinic.
Other health insurance will usually cover the cost of your urgent care visit though and you may have to pay out of pocket for the urgent care visit.
The Urgent Care centers are usually much cheaper than the emergency room and are sometimes less busy.