Abstract Marine Isotope Stage 3 (MIS 3) is characterized by significant millennial-scale climatic oscillations between cold stadials and mild interstadials, which presents a valuable case for understanding hydrological response to abrupt climate change. Through a set of coupled model simulations, our results broadly show an antiphased interhemispheric change in land monsoonal precipitation during the present-day relative to MIS 3 interstadial and the stadial–interstadial transition, with a general decrease in the Northern Hemisphere but an increase in the Southern Hemisphere. The antiphased pattern is largely caused by the change in orbital insolation during the present-day relative to MIS 3 interstadial, whereas by the weakened Atlantic meridional overturning circulation during the interstadial–stadial transition. However, there are obvious discrepancies in precipitation response and underlying mechanisms among individual monsoon domains and across different periods. Based on the moisture budget analysis, we indicate that the dynamic factor mainly explains the decreased monsoonal rainfall in the Northern Hemisphere during the present-day relative to the MIS 3 interstadial, whereas the thermodynamic term is largely responsible for the increased precipitation in the Southern Hemisphere. In contrast, the dynamic factor plays an important role in the variation of precipitation over all the monsoon zones from the MIS 3 interstadial to stadial states, with the thermodynamic term mainly contributing to the decreased tropical monsoonal precipitation in the colder Northern Hemisphere. Our results help improve the understanding of global monsoon variations under intermediate glacial climate conditions and shed light on their behaviors under potentially rapid climate change in the future.