Minority Community Public Health Emergency Response Act of 2020 This bill establishes a grant program for COVID-19 (i.e., coronavirus disease 2019) preparedness and response in medically underserved communities where the disease disproportionally affects racial and ethnic minority groups. It also modifies the scope and administration of demonstration models carried out by the Center for Medicare and Medicaid Innovation (CMMI) to address health inequity. With respect to the grant program, the Department of Health and Human Services (HHS) must award grants to government entities, giving priority to local governments and county health departments, for contact tracing, other public health activities, and the provision of nutrition assistance and quarantine housing. HHS may also support planning activities for entities that intend to apply for these grants. As a condition for receiving funding, grantees must establish, or designate an existing body as, a COVID-19/infectious disease planning council. The council must reflect the demographics of the populations most impacted by COVID-19, and its responsibilities shall include developing a plan for the delivery of health care and support services to address COVID-19 and establishing priorities for allocating funding. In addition, the CMMI must test a payment model that addresses social determinants of health and health disparities, particularly with respect to minorities, underserved areas, and high-risk individuals. The bill also generally incorporates consideration of such factors into the selection, implementation, and evaluation of other models, including the decision as to whether to expand a model's duration and scope.