Owning to the rapid development of computer technologies, an increasing number of relational data have been emerging in modern biomedical research. Many network-based learning methods have been proposed to perform analysis on such data, which provide people a deep understanding of topology and knowledge behind the biomedical networks and benefit a lot of applications for human healthcare. However, most network-based methods suffer from high computational and space cost. There remain challenges on handling high dimensionality and sparsity of the biomedical networks. The latest advances in network embedding technologies provide new effective paradigms to solve the network analysis problem. It converts network into a low-dimensional space while maximally preserves structural properties. In this way, downstream tasks such as link prediction and node classification can be done by traditional machine learning methods. In this survey, we conduct a comprehensive review of the literature on applying network embedding to advance the biomedical domain. We first briefly introduce the widely used network embedding models. After that, we carefully discuss how the network embedding approaches were performed on biomedical networks as well as how they accelerated the downstream tasks in biomedical science. Finally, we discuss challenges the existing network embedding applications in biomedical domains are faced with and suggest several promising future directions for a better improvement in human healthcare.