Stratospheric aerosol injection (SAI) has been proposed as a potential supplement to mitigate some climate impacts of anthropogenic warming. Using Community Earth System Model ensemble simulation results, we analyze the response of temperature and precipitation extremes to two different SAI strategies: one injects SO2 at the equator to stabilize global mean temperature and the other injects SO2 at multiple locations to stabilize global mean temperature as well as the interhemispheric and equator‐to‐pole temperature gradients. Our analysis shows that in the late 21st century, compared with the present‐day climate, both equatorial and multi‐location injection lead to reduced hot extremes in the tropics, corresponding to overcooling of the mean climate state. In mid‐to‐high latitude regions, in comparison to the present‐day climate, substantial decreases in cold extremes are observed under both equatorial and multi‐location injection, corresponding to residual winter warming of the mean climate state. Both equatorial and multi‐location injection reduce precipitation extremes in the tropics below the present‐day level, associated with the decrease in mean precipitation. Overall, for most regions, temperature and precipitation extremes show reduced change in response to multi‐location injection than to equatorial injection, corresponding to reduced mean climate change for multi‐location injection. In comparison with equatorial injection, in response to multi‐location injection, most land regions experience fewer years with significant change in cold extremes from the present‐day level, and most tropical regions experience fewer years with significant change in hot extremes. The design of SAI strategies to mitigate anthropogenic climate extremes merits further study.