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Extreme hydrological events in the Danube river basin may severely impact human populations, aquatic organisms and economic activity. One often characterizes the joint structure of extreme events by using the theory of multivariate and spatial extremes and its asymptotically justified models. There is interest, however, in cascading extreme events and whether one event causes another. We argue that an improved understanding of the mechanism underlying severe events is achieved by combining extreme value modelling and causal discovery. We construct a causal inference method relying on the notion of the Kolmogorov complexity of extreme conditional quantiles. Tail quantities are derived by using multivariate extreme value models, and causal-induced asymmetries in the data are explored through the minimum description length principle. Our method CausEV for causality for extreme values uncovers causal relationships between summer extreme river discharges in the upper Danube basin and finds significant causal links between the Danube and its Alpine tributary Lech.