A consequence of the interconnectedness of global supply chains is that disturbances in one location can propagate between continents. This means that for companies to manage climate risks, it is important not just to assess risks in operation locations, but also throughout supply chains. In this paper, we analyse how 14 Swedish large export-oriented businesses view and address risks from physical climate impacts on their international supply chains. We find that climate change is not considered a priority risk and there is little evidence of risk management strategies implemented at the operational level. Businesses fail to see a clear causality between climate change as a global phenomenon and operational risks in the supply chain. Furthermore, the complicated structures of many supply chains make comprehensive risk assessment and management very resource-demanding. We conclude that there is a need for novel strategies to improve businesses’ capabilities to assess emerging risks from climate change.