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Climate models face limitations in their ability to accurately represent highly variable atmospheric phenomena. To resolve fine‐scale physical processes, allowing for local impact assessments, downscaling techniques are essential. We propose spateGAN, a novel approach for spatio‐temporal downscaling of precipitation data using conditional generative adversarial networks. Our method is based on a video super‐resolution approach and trained on 10 years of country‐wide radar observations for Germany. It simultaneously increases the spatial and temporal resolution of coarsened precipitation observations from 32 to 2 km and from 1 hr to 10 min. Our experiments indicate that the ensembles of generated temporally consistent rainfall fields are in high agreement with the observational data. Spatial structures with plausible advection were accurately generated. Compared to trilinear interpolation and a classical convolutional neural network, the generative model reconstructs the resolution‐dependent extreme value distribution with high skill. It showed a high fractions skill score of 0.6 (spatio‐temporal scale: 32 km and 1 hr) for rainfall intensities over 15 mm h−1 and a low relative bias of 3.35%. A power spectrum analysis confirmed that the probabilistic downscaling ability of our model further increased its skill. We observed that neural network predictions may be interspersed by recurrent structures not related to rainfall climatology, which should be a known issue for future studies. We were able to mitigate them by using an appropriate model architecture and model selection process. Our findings suggest that spateGAN offers the potential to complement and further advance the development of climate model downscaling techniques, due to its performance and computational efficiency. Plain Language Summary: Natural disasters like floods, hail, or landslides originate from precipitation. Global climate models are an important tool to understand these hazards and derive expected changes in a future climate. However, they operate on spatial and temporal scales that limit the regional ability to reflect their small‐scale characteristics. This has led to the development of dynamical and statistical downscaling methods. Due to their computational efficiency, machine learning algorithms recently got increased attention as a method for improving the spatial resolution of climate data. Here, we describe a new deep learning model that allows to simultaneously increasing both the temporal and spatial resolution of precipitation data. Our presented approach enhances the spatial resolution by a factor of 16 and the temporal resolution by a factor of 6. The generated rain fields are hardly identifiable as artificially generated and exhibit the typical structure, movement, and distribution of observed rain fields. Key Points: High performance simultaneous spatial and temporal precipitation downscaling enabled by 3D convolution approachGeneration of realistic high‐resolution ensembles using probabilistic conditional generative adversarial networksLow computational effort compared to dynamical downscaling approaches [ABSTRACT FROM AUTHOR]