Climate model studies in which CO2-induced global warming is offset by engineered decreases of incoming solar radiation are generally robust in their prediction of reduced amounts of global precipitation. While this precipitation response has been explained on the basis of changes in net radiation controlling evaporative processes at the surface, there has been relatively little consideration of the relative role of biogeochemical carbon-cycle interactions. To address this issue, we employ an Earth System Model that includes oceanic and terrestrial carbon components to isolate the impact of biogeochemical carbon coupling on the precipitation response in geoengineering experiments for two types of solar radiation management. We show that carbon coupling is responsible for a large fraction of the global precipitation reduction in such geoengineering experiments and that the primary effect comes from reduced transpiration through the leaves of plants and trees in the terrestrial component of the carbon cycle due to elevated CO2. Our results suggest that biogeochemical interactions are as important as changes in net radiation and that climate models that do not account for such carbon coupling may significantly underestimate precipitation reductions in a geoengineered world.