Flood risk is projected to increase under future warming climates due to an enhanced hydrological cycle. Solar geoengineering is known to reduce precipitation and slow down the hydrological cycle and may therefore be expected to offset increased flood risk. We examine this hypothesis using streamflow and river discharge responses to Representative Concentration Pathway 4.5 (RCP4.5) and the Geoengineering Model Intercomparison Project (GeoMIP) G4 scenarios. Compared with RCP4.5, streamflow on the western sides of Eurasia and North America is increased under G4, while the eastern sides see a decrease. In the Southern Hemisphere, the northern parts of landmasses have lower streamflow under G4, and streamflow of southern parts increases relative to RCP4.5. We furthermore calculate changes in 30-, 50-, and 100-year flood return periods relative to the historical (1960-1999) period under the RCP4.5 and G4 scenarios. Similar spatial patterns are produced for each return period, although those under G4 are closer to historical values than under RCP4.5. Hence, in general, solar geoengineering does appear to reduce flood risk in most regions, but the overall effects are largely determined by this large-scale geographic pattern. Although G4 stratospheric aerosol geoengineering ameliorates the Amazon drying under RCP4.5, with a weak increase in soil moisture, the decreased runoff and streamflow leads to an increased flood return period under G4 compared with RCP4.5.