The quantity of medical waste produced by municipalities is on the rise, potentially presenting significant hazards to both the environment and human health. Developing a robust supply chain network for managing municipal medical waste is important for society, especially during a pandemic like COVID-19. In supply chain network design, factors such as the collection of non-infectious waste, transporting infectious waste from hospitals to disposal facilities, revenue generation from waste-to-energy initiatives, and the potential for pandemic outbreaks are often overlooked. Hence, in this study, we design a model incorporating COVID-19 parameters to mitigate the spread of the virus while designing an effective municipal medical waste supply chain network during a pandemic. The proposed model is multi-objective, multi-echelon, multi-commodity and involves coalition-based cooperation. The first objective function aims to minimize total costs, while the second objective pertains to minimizing the risk of a COVID-19 outbreak. We identify optimal collaboration among municipal medical waste collection centers to maximize cost savings. The COVID-19 prevalence risk level by the waste in each zone is calculated pursuant to their inhabitants. Additionally, we analyze a system dynamic simulation framework to forecast waste generation levels amid COVID-19 conditions. A metaheuristic based on the Non-dominated Sorting Genetic Algorithm II is used to solve the problem and is benchmarked against exact solutions. To illustrate our approach, we present a case study focused on Tehran, Iran. The results show that an increase in the amount of generated waste leads to an increase in the total costs of the supply chain.