Transition from a linear to a circular economy (CE) is a challenging process for a sustainable supply chain, and innovative process approaches and technologies are needed to deal with the risks involved. Industry 4.0 principles have great potential to achieve optimal sustainable supply chain solutions and are expected to add value to sustainable supply chain operations by increasing efficiency and resource utilisation. Therefore, Industry 4.0 supports companies transitioning to a CE through improving the efficiency and sustainability of their supply chain management. Thus, the purpose of this paper is to investigate the potential risks of the transition from a linear to a CE, with proposed Industry 4.0-based responses from an operations management perspective within the sustainable supply chain. Implementation of the study was conducted in a logistics company in Turkey. An integrated MCDM (Multi-criteria Decision Making) approach was based on Fuzzy AHP, and TODIM was used to analyse the association between risks and responses. According to the findings, the most important Industry 4.0-based responses are the integrated business processes for cross-functional collaboration, modular processes for simplification and standardisation, and continuous monitoring of the cost and performance throughout the supply chain by big data and analytics. This study may assist managers in managing risks in supply chain operations during the transition from a linear to a CE through Industry 4.0 based responses. The main contribution of this study is a greater understanding of the risks related to the transition from a linear to a circular economy, and proposals for Industry 4.0-based responses as a means of overcoming these risks in a sustainable supply chain context.