Medical waste management (MWM) is an important and necessary problem in the COVID-19 situation for treatment staff. When the number of infectious patients grows up, the amount of MWMs increases day by day. We present medical waste chain network design (MWCND) that contains health center (HC), waste segregation (WS), waste purchase contractor (WPC), and landfill. We propose to locate WS to decrease waste and recover them and send them to the WPC. Recovering medical waste like metal and plastic can help the environment and return to the production cycle. Therefore, we proposed a novel viable MWCND by a novel two-stage robust stochastic programming that considers resiliency (flexibility and network complexity) and sustainable (energy and environment) requirements. Therefore, we try to consider risks by conditional value at risk (CVaR) and improve robustness and agility to demand fluctuation and network. We utilize and solve it by GAMS CPLEX solver. The results show that by increasing the conservative coefficient, the confidence level of CVaR and waste recovery coefficient increases cost function and population risk. Moreover, increasing demand and scale of the problem makes to increase the cost function.