Cyclonic atmospheric vortices of varying intensity, collectively known as low-pressure systems (LPS), travel northwest across central India and produce more than half of the precipitation received by that fertile region and its ~600 million inhabitants. Yet, future changes in LPS activity are poorly understood, due in part to inadequate representation of these storms in current climate models. Using a high-resolution atmospheric general circulation model that realistically simulates the genesis distribution of LPS, here we show that Indian monsoon LPS activity declines about 45% by the late 21st century in simulations of a business-as-usual emission scenario. The distribution of LPS genesis shifts poleward as it weakens, with oceanic genesis decreasing by ~60% and continental genesis increasing by ~10%; over land the increase in storm counts is accompanied by a shift toward lower storm wind speeds. The weakening and poleward shift of the genesis distribution in a warmer climate are confirmed and attributed, via a statistical model, to the reduction and poleward shift of low-level absolute vorticity over the monsoon region, which in turn are robust features of most coupled model projections. The poleward shift in LPS activity results in an increased frequency of extreme precipitation events over northern India.