The early detection of infectious disease outbreaks is a crucial task to protect population health. To this end, public health surveillance systems have been established to systematically collect and analyse infectious disease data. A variety of statistical tools are available, which detect potential outbreaks as abberations from an expected endemic level using these data. Here, we present supervised hidden Markov models for disease outbreak detection, which use reported outbreaks that are routinely collected in the German infectious disease surveillance system and have not been leveraged so far. This allows to directly integrate labeled outbreak data in a statistical time series model for outbreak detection. We evaluate our model using real Salmonella and Campylobacter data, as well as simulations. The proposed supervised learning approach performs substantially better than unsupervised learning and on par with or better than a state-of-the-art approach, which is applied in multiple European countries including Germany.