Identifying the potential associations among drugs, microbes and diseases is of great significance in exploring the pathogenesis and improving precision medicine. There are plenty of computational methods for pair-wise association prediction, such as drug-microbe and microbe-disease associations, but few methods focus on the higher-order triple-wise drug-microbe-disease (DMD) associations. Driven by the advancement of hypergraph neural networks (HGNNs), we expect them to fully capture high-order interaction patterns behind the hypergraph formulated by DMD associations and realize sound prediction performance. However, the confirmed DMD associations are insufficient due to the high cost of in vitro screening, which forms a sparse DMD hypergraph and thus brings in suboptimal generalization ability. To mitigate the limitation, we propose a Multi-view Contrastive Learning Hypergraph Neural Network, named MCHNN, for DMD association prediction. We design a novel multi-view contrastive learning on the DMD hypergraph as an auxiliary task, which guides the HGNN to learn more discriminative representations and enhances the generalization ability. Extensive computational experiments show that MCHNN achieves satisfactory performance in DMD association prediction and, more importantly, demonstrate the effectiveness of our devised multi-view contrastive learning on the sparse DMD hypergraph.