We propose a probabilistic deep learning approach for the prediction of maximum water depth hazard maps at high spatial resolutions, which assigns well-calibrated uncertainty estimates to every predicted water depth. Efficient, accurate, and trustworthy methods for urban flood management have become increasingly important due to higher rainfall intensity caused by climate change, the expansion of cities, and changes in land use. While physically based flood models can provide reliable forecasts for water depth at every location of a catchment, their high computational burden is hindering their application to large urban areas at high spatial resolution. While deep learning models have been used to address this issue, a disadvantage is that they are often perceived as “black-box” models and are overconfident about their predictions, therefore decreasing their reliability. Our deep learning model learns the underlying phenomena a priori from simulated hydrodynamic data, obviating the need for manual parameter setting for every new rainfall event at test time. The only inputs needed at the test time are a rainfall forecast and parameters of the terrain such as a digital elevation model to predict the maximum water depth with uncertainty estimates for complete rainfall events. We validate the accuracy and generalisation capabilities of our approach through experiments on a dataset consisting of catchments within Switzerland and Portugal and 18 rainfall patterns. Our method produces flood hazard maps at 1 m resolution and achieves mean absolute errors as low as 21 cm for extreme flood cases with water above 1 m. Most importantly, we demonstrate that our approach is able to provide an uncertainty estimate for every water depth within the predicted hazard map, thus increasing the model’s trustworthiness during flooding events.