Among the most urgent challenges in future climate change scenarios is accurately predicting the magnitude to which precipitation extremes will intensify. Analogous changes have been reported for an episode of millennial-scale 5 °C warming, termed the Palaeocene-Eocene Thermal Maximum (PETM; 56 Ma), providing independent constraints on hydrological response to global warming. However, quantifying hydrologic extremes during geologic global warming analogs has proven difficult. Here we show that water discharge increased by at least 1.35 and potentially up to 14 times during the early phase of the PETM in northern Spain. We base these estimates on analyses of channel dimensions, sediment grain size, and palaeochannel gradients across the early PETM, which is regionally marked by an abrupt transition from overbank palaeosol deposits to conglomeratic fluvial sequences. We infer that extreme floods and channel mobility quickly denuded surrounding soil-mantled landscapes, plausibly enhanced by regional vegetation decline, and exported enormous quantities of terrigenous material towards the ocean. These results support hypotheses that extreme rainfall events and associated risks of flooding increase with global warming at similar, but potentially at much higher, magnitudes than currently predicted.