It has been suggested that the Sun may evolve into a period of lower activity over the 21st century. This study examines the potential climate impacts of the onset of an extreme “Maunder Minimum-like” grand solar minimum using a comprehensive global climate model. Over the second half of the 21st century, the scenario assumes a decrease in total solar irradiance of 0.12% compared to a reference Representative Concentration Pathway 8.5 experiment. The decrease in solar irradiance cools the stratopause (∼1 hPa) in the annual and global mean by 1.2 K. The impact on global mean near-surface temperature is small (∼−0.1 K), but larger changes in regional climate occur during the stratospheric dynamically active seasons. In Northern Hemisphere wintertime, there is a weakening of the stratospheric westerly jet by up to ∼3–4 m s−1, with the largest changes occurring in January–February. This is accompanied by a deepening of the Aleutian Low at the surface and an increase in blocking over Northern Europe and the North Pacific. There is also an equatorward shift in the Southern Hemisphere midlatitude eddy-driven jet in austral spring. The occurrence of an amplified regional response during winter and spring suggests a contribution from a top-down pathway for solar-climate coupling; this is tested using an experiment in which ultraviolet (200–320 nm) radiation is decreased in isolation of other changes. The results show that a large decline in solar activity over the 21st century could have important impacts on the stratosphere and regional surface climate.