The outbreak of the deadly coronavirus, which is increasing the number of victims every day, has created many changes in today’s world. The use of various masks is the most important social tool against this virus. Given the importance of rapid and quality supply of masks in the current situation, it is necessary to study supply chain in particular. In this research, the design of a closed chain supply chain network for different types of masks is assessed. The studied supply chain includes suppliers, manufacturers, distributors, and retailers in the forward flow and collection centers, separate centers, recycling centers, and disposal centers in the backward flow. In this regard, a multi-objective mathematical model with the objectives of increasing the total profit and reducing the total environmental impact, and maximizing social responsibility is presented. The optimization of this mathematical model has been done using a fuzzy optimization approach in GAMS software. The results of this study show that maximizing the total profit and minimizing the environmental effects and maximizing social responsibility are in contrast to each other. In addition, the sensitivity analysis indicated that the customers’ demand can affect all aspects of the sustainable supply chain simultaneously.