This paper aims to assess the relationship between Industry 4.0 (I4.0) and the circular economy that could contribute to supply chain management performance. To achieve this, a combination of the interpretative structural modelling (ISM) and (cross-impact matrix multiplication applied to classification) MICMAC approach was used to establish the interrelationships between these topics. The developed analysis reveals that there are 19 constructs capable of elucidating this relationship and that there is a hierarchy between these constructs, which are presented in a structural model. Further, the different levels of dependency and driving power are compared in a cluster diagram. As the main result, it was found that there is a strong mutual relationship between the basic technologies. The use of Internet of Things and cloud computing technologies influences the collection of large amounts of data, leading to big data, which in turn influence the use of data analytics tools to obtain competitive advantages. These outcomes may contribute to managers’ more assertive decision-making regarding the selection, implementation, and evaluation of projects adopting Industry 4.0 technologies and circular economy approaches in supply chains. Moreover, our study could be the basis for future empirical research to investigate how companies incorporate Industry 4.0 technologies into their processes and how this influences the quest for sustainable supply chains.