Given the crucial role of the supplier selection problem (SSP) in today’s competitive business environment, the present study investigates the SSP by considering the leagile, sustainability, and Industry 4.0 (I4.0) indicators for the medical devices industry (MDI). In this regard, at the outset, the list of criteria and sub-criteria is provided based on the literature and experts’ opinions. Then, the importance of the indicators is measured utilizing the rough best–worst method (RBWM). In the next step, the potential suppliers are ranked employing the multi-attributive border approximation area comparison (IR-MABAC) method. Due to the crucial role of medical devices during the COVID-19 outbreak, the present work selects a project-based organization in this industry as a case study. The obtained results show that agility and sustainability are the most important criteria, and manufacturing flexibility, cost, reliability, smart factory, and quality are the most important sub-criteria. The main theoretical contributions of this study are considering the leagile, sustainability, and I4.0 criteria in the SSP and employing the hybrid RBWM-IR-MABAC method in this area for the first time. On the other side, The results of this research can help supply chain managers to become more familiar with the sustainability, agility, leanness, and I4.0 criteria in the business environment.