Solar geoengineering is receiving increased policy attention as a potential tool to offset climate warming. While climate responses to geoengineering have been studied in detail, the potential biodiversity consequences are largely unknown. To avoid extinction, species must either adapt or move to track shifting climates. Here, we assess the effects of the rapid implementation, continuation and sudden termination of geoengineering on climate velocities—the speeds and directions that species would need to move to track changes in climate. Compared to a moderate climate change scenario (RCP4.5), rapid geoengineering implementation reduces temperature velocities towards zero in terrestrial biodiversity hotspots. In contrast, sudden termination increases both ocean and land temperature velocities to unprecedented speeds (global medians >10 km yr−1) that are more than double the temperature velocities for recent and future climate change in global biodiversity hotspots. Furthermore, as climate velocities more than double in speed, rapid climate fragmentation occurs in biomes such as temperate grasslands and forests where temperature and precipitation velocity vectors diverge spatially by >90°. Rapid geoengineering termination would significantly increase the threats to biodiversity from climate change.