Climate change is likely to lead to more frequent and more severe supply and demand shocks that will present a challenge to monetary policy formulation. The main objective of the paper is to investigate how climate shocks affect consumer prices in a broad range of countries over a long period using local projection methods. It finds that the impact of climate shocks on inflation depends on the type and intensity of shocks, country income level, and monetary policy regime. Specifically, droughts tend to have the highest overall positive impact on inflation, reflecting rising food prices. Interestingly, floods tend to have a dampening impact on inflation, pointing to the predominance of demand shocks in this case. Over the long run, the dominant monetary policy paradigm of flexible inflation targeting faced with supply-induced climate shocks may become increasingly ineffective, especially in LIDCs. More research is needed to find viable alternative monetary policy frameworks.