In the face of anthropogenic warming, drought poses an escalating threat to food production. C4 plants offer promise in addressing this threat. C4 leaves operate a biochemical CO2 concentrating mechanism that exchanges metabolites between two partially isolated compartments (mesophyll and bundle sheath), which confers high-productivity potential in hot climates boosting water use efficiency. However, when C4 leaves experience dehydration, photosynthesis plummets. This paper explores the physiological mechanisms behind this decline. In a fast dehydration experiment, we measured the fluxes and isotopic composition of water and CO2 in the gas exchanged by leaves, and we interpreted results using a novel biochemical model and analysis of elasticity. Our findings show that, while CO2 supply to the mesophyll and to the bundle sheath persisted during dehydration, there was a decrease in CO2 conductance at the bundle sheath-mesophyll interface. We interpret this as causing a slowdown of intercellular metabolite exchange - an essential feature of C4 photosynthesis. This would impede the supply of reducing power to the bundle sheath, leading to phosphoglycerate accumulation and feedback inhibition of Rubisco carboxylation. The interplay between this rapid sensitivity and the effectiveness of coping strategies that C4 plants deploy may be an overlooked driver of their competitive performance.