The supplier selection problem is one of the most important issues in supply chain management. So, many papers have investigated the mentioned problem. However, the related literature shows that researchers had less attention to the sustainability and resilience aspects based on the customer preferences in supplier selection problem. To cover this gap, this research tries to investigate the customer-based sustainable-resilient supplier selection problem. In this way, a Markovian-based fuzzy decision-making method is proposed. At the outset, the customer preferences are evaluated using a combination of the quality function deployment and the Markov transition matrix. Then, by combining the transition matrix and the fuzzy best–worst method, the weights of the indicators are calculated. Finally, the decision matrix is formed and the performance of suppliers is measured based on the multiplication of the decision matrix and vector of sub-criteria weights. Regarding the recent pandemic disruption (COVID-19), the importance of online marketplaces is highlighted more than the past. Hence, this study considers an online marketplace as a case study. Results show that in a pandemic situation, the preferences of customers when they cannot go shopping normally will change after a while. Based on the Markov steady state, these changes are from the priority of price, availability, and performance in initial time to serviceability, reliability, and availability in the future. Finally, based on the FBWM results, from the customer point of view, the top five sub-criteria for sustainable-resilient supplier selection include cost, quality, delivery, responsiveness, and service. So, based on these priorities, the case study potential suppliers are prioritized, respectively.