Accurately identifying microbe-drug associations plays a critical role in drug development and precision medicine. Considering that the conventional wet-lab method is time-consuming, labor-intensive and expensive, computational approach is an alternative choice. The increasing availability of numerous biological data provides a great opportunity to systematically understand complex interaction mechanisms between microbes and drugs. However, few computational methods have been developed for microbe drug prediction. In this work, we leverage multiple sources of biomedical data to construct a heterogeneous network for microbes and drugs, including drug-drug interactions, microbe-microbe interactions and microbe-drug associations. And then we propose a novel Heterogeneous Network Embedding Representation framework for Microbe-Drug Association prediction, named (HNERMDA), by combining metapath2vec with bipartite network recommendation. In this framework, we introduce metapath2vec, a heterogeneous network representation learning method, to learn low-dimensional embedding representations for microbes and drugs. Following that, we further design a bias bipartite network projection recommendation algorithm to improve prediction accuracy. Comprehensive experiments on two datasets, named MDAD and aBiofilm, demonstrated that our model consistently outperformed five baseline methods in three types of cross-validations. Case study on two popular drugs (i.e., Ciprofloxacin and Pefloxacin) further validated the effectiveness of our HNERMDA model in inferring potential target microbes for drugs.