Healthcare systems worldwide are facing problems in providing health care to patients in a pandemic caused by the SARS-CoV-2 virus (COVID-19). The pandemic causes an extreme disease to spread with fluctuating needs among patients, which significantly affect the capacity and overall performance of healthcare systems. In addition, its impact on the sustainability of the entire economic and social system is enormous and certain sustainable management strategies need to be selected. To meet the challenges of the COVID-19 pandemic and ensure sustainable performance, national healthcare systems must adapt to new circumstances. This paper proposes an original multi-criteria methodology for the sustainable selection of strategic guidelines for the reorganization of a healthcare system under the conditions of the COVID-19 pandemic. The selection of an appropriate strategic guideline is made on the basis of defined criteria and depending on infection capacity and pandemic spread risk. The criteria for the evaluation of strategic guidelines were defined on the basis of a survey in which the medical personnel engaged in the crisis response team during the COVID-19 pandemic in the Republic of Serbia participated. The Level-Based Weight Assessment (LBWA) model and Measuring Attractiveness by a Categorical-Based Evaluation Technique (MACBETH) method were used to determine the weight coefficient criteria, while a novel fuzzy Ranking of Alternatives through Functional Mapping of Criterion Subintervals into a Single Interval (RAFSI) model was used to evaluate the strategic guidelines. The proposed multi-criteria methodology was tested in a case study in the Republic of Serbia. The validity of the proposed methodology is shown through the simulation of changes in input parameters of Bonferroni aggregation functions and through a comparison with other multi-criteria methodologies.