In recent years, quantum physics-inspired tensor networks have seen an explosion in use cases.While these networks were originally developed to model many-body quantum systems, their usage has expanded into the field of machine learning, where they are often used as an alternative to neural networks.In a similar way, the neuroscience-based theory of active inference, a general framework for behavior and learning in autonomous agents, has started branching out into machine learning.Since every aspect of an active inference model, such as the latent space structure, must be manually defined, efforts have been made to learn state space representations automatically from observations using deep neural networks.In this work, we show that tensor networks can be employed to learn an active inference model with a discrete observation space.We demonstrate our method on the T-maze problem and show that the agent acts Bayes optimal as expected under active inference.