Networks found in the real-world are numerous and varied. A common type of network is the heterogeneous network, where the nodes (and edges) can be of different types. Accordingly, there have been efforts at learning representations of these heterogeneous networks in low-dimensional space. However, most of the existing heterogeneous network embedding methods suffer from the following two drawbacks: (1) The target space is usually Euclidean. Conversely, many recent works have shown that complex networks may have hyperbolic latent anatomy, which is non-Euclidean. (2) These methods usually rely on meta-paths, which require domain-specific prior knowledge for meta-path selection. Additionally, different down-streaming tasks on the same network might require different meta-paths in order to generate task-specific embeddings. In this paper, we propose a novel self-guided random walk method that does not require meta-path for embedding heterogeneous networks into hyperbolic space. We conduct thorough experiments for the tasks of network reconstruction and link prediction on two public datasets, showing that our model outperforms a variety of well-known baselines across all tasks.