Fusarium head blight (FHB) of wheat, mainly caused by Fusarium graminearum Schwabe, is an emerging threat to wheat production in Korea under a changing climate. The disease occurrence and accumulation of associated trichothecene mycotoxins in wheat kernels strongly coincide with warm and wet environments during flowering. Recently, the International Panel for Climate Change released the 6th Coupled Model Intercomparison Project (CMIP6) climate change scenarios with shared socioeconomic pathways (SSPs). In this study, we adopted GIBSIM, an existing mechanistic model developed in Brazil to estimate the risk infection index of wheat FHB, to simulate the potential FHB epidemics in Korea using the SSP245 and SSP585 scenarios of CMIP6. The GIBSIM model simulates FHB infection risk from airborne inoculum density and infection frequency using temperature, precipitation, and relative humidity during the flowering period. First, wheat heading dates, during which GIBSIM runs, were predicted over suitable areas of winter wheat cultivation using a crop development rate model for wheat phenology and downscaled SSP scenarios. Second, an integrated model combining all results of wheat suitability, heading dates, and FHB infection risks from the SSP scenarios showed a gradual increase in FHB epidemics towards 2100, with different temporal and spatial patterns of varying magnitudes depending on the scenarios. These results indicate that proactive management strategies need to be seriously considered in the near future to minimize the potential impacts of the FHB epidemic under climate change in Korea. Therefore, available wheat cultivars with early or late heading dates were used in the model simulations as a realistic adaptation measure. As a result, wheat cultivars with early heading dates showed significant decreases in FHB epidemics in future periods, emphasizing the importance of effective adaptation measures against the projected increase in FHB epidemics in Korea under climate change.