Artificial Intelligence (AI) has emerged as a complementary technology in supply chain research. However, the majority of AI approaches explored in this context afford little to no explainability, which is a significant barrier to a broader adoption of AI in supply chains. In recent years, the need for explainability has been a strong impetus for research in hybrid AI methodologies that combine neural architectures with logic-based reasoning, which are collectively referred to as Neurosymbolic AI. The aim of this paper is to provide a comprehensive overview of supply chain management literature that employes approaches within the neurosymbolic AI spectrum. To that end, a systematic review is conducted, followed by bibliometric, descriptive and thematic analyses on the identified studies. Our findings indicate that researchers have primarily focused on the limited subset of neurofuzzy approaches, while some supply chain applications, such as performance evaluation and sustainability, and sectors such as pharmaceutical and construction have received less attention. To help address these gaps, we propose five pillars of neurosymbolic AI research for supply chains and provide three use cases of applying unexplored neurosymoblic AI approaches to address typical problems in supply chain management, including a discussion of prerequisites for adopting such technologies. We envision that the findings and contributions of this survey will help encourage further research in neurosymbolic AI for supply chains and increase adoption of such technologies within supply chain practice.