The continuous emergence of drug-target interaction data provides an opportunity to construct a biological network for systematically discovering unknown interactions. However, this is challenging due to complex and heterogeneous correlations between drug and target. Here, we describe a heterogeneous hypergraph-based framework for drug-target interaction (HHDTI) predictions by modeling biological networks through a hypergraph, where each vertex represents a drug or a target and a hyperedge indicates existing similar interactions or associations between the connected vertices. The hypergraph is then trained to generate suitably structured embeddings for discovering unknown interactions. Comprehensive experiments performed on four public datasets demonstrate that HHDTI achieves significant and consistently improved predictions compared with state-of-the-art methods. Our analysis indicates that this superior performance is due to the ability to integrate heterogeneous high-order information from the hypergraph learning. These results suggest that HHDTI is a scalable and practical tool for uncovering novel drug-target interactions.