We present a novel approach to probabilistic electricity price forecasting which utilizes distributional neural networks. The model structure is based on a deep neural network containing a so-called probability layer, i.e., the outputs of the network are parameters of the normal or Johnson’s SU distribution. To validate our approach, we conduct a comprehensive forecasting study complemented by a realistic trading simulation with day-ahead electricity prices in the German market. The proposed distributional deep neural network outperforms state-of-the-art benchmarks by over 7% in terms of the continuous ranked probability score and by 8% in terms of the per-transaction profits. The obtained results not only emphasize the importance of higher moments when modeling volatile electricity prices, but also – given that probabilistic forecasting is the essence of risk management – provide important implications for managing portfolios in the power sector.