Globally, the pandemic of COVID-19 has penetrated all spheres of human endeavors, and noteworthy is the tremendous increase in the volume of healthcare wastes generated in Nigeria. There has been an increase in medical waste materials produced as a result of the extensive use of both disposable personal protective equipment (PPE), such as face shields and nose and face masks, and highly infectious waste materials, such as contaminated syringes, needles, and soiled bandages from diagnosed positive cases. Despite the huge volume in waste generation, a standardized evaluation framework is currently lacking in the management of medical wastes in Nigeria. This study has developed a novel assessment framework for managing medical wastes, which is curated from the technical guidelines of the World Health Organization (WHO). The applicability of the framework was examined on seven designated public and private-owned hospitals in Ota. The fuzzy analytical hierarchy process (FAHP) and analytical hierarchy process (AHP) approaches of multi-criteria decision analysis were utilized in modelling an evaluation framework for the objective of medical waste management. Carefully designed interview questionnaires, observations, and site visits were carried out to obtain data from healthcare professionals in Ota. Results show that waste segregation was practiced more decisively in private hospitals than public hospitals. Waste segregation is established as a key determinant in implementing an effective waste management system in any healthcare facility. The success of waste segregation in healthcare institutions is highly dependent on good hospital management, organizational policies, efficient budget planning for waste management, and the operational running cost. Disposal methods investigated were mostly open burning and incessant dumping for most public health care centers. Deficient waste management practices were observed in waste disposal, waste transportation, storage, and organizational policies. While the awareness and capacity building on occupational safety practices and environmental public health is widely known by health workers and waste handlers, compliance and enforcement are critical challenges. The validation of results using fuzzy TOPSIS and a sensitivity analysis shows a high degree of the consistency, stability, and robustness of the model. Findings from the present study can aid decision making, as this will benefit policy makers and key stakeholders in developing more comprehensive and effective medical waste management guidelines in Nigeria. In addition, future decision-making studies could augment the results from the current research by assessing the impact of the pandemic preparedness and response on medical waste management.