Countries can suffer supply chain disruptions and important economic losses when their trade partners are hit by natural disasters. As climate change intensifies, the frequency and intensity of climate-related extreme events are expected to increase, leading to an increase in this cross-border risk. However, the magnitude of this risk, and the relative exposure of different countries and different sectors is not clear. Here, we combine international trade data with climate risk indices to measure the exposure of countries’ economies to foreign climate-related hazards, in the context of climate change. We find that this indirect exposure is highly heterogeneous between countries. While its geographical pattern generally differs from those of direct climate change impacts, several countries suffer a double exposure and are exposed to both risks, as a result of regional trade integration and geographic concentration of climate risks. Moreover, almost every country faces high exposure for at least one broad category of imports.