The identification of drug sensitivity to mRNA interactions is crucial for drug development and disease treatment, but traditional experimental methods for verifying mRNA-drug sensitivity associations are labor-intensive and time-consuming. In this study, we present a hypergraph contrastive learning approach, HGCLMDA, to predict potential mRNA-drug sensitivity associations. HGCLMDA integrates a graph convolutional network-based method with a hypergraph convolutional network to mine high-order relationships between mRNA-drug association pairs. The proposed cross-view contrastive learning architecture improves the model's learning ability, and the inner product is used to obtain the mRNA-drug sensitivity association score. Our experiments on three mRNA-drug sensitivity association data sets show that HGCLMDA outperforms traditional graph convolutional network-based methods, graph augmentation-based contrastive learning methods, and state-of-the-art association prediction methods. The visualization experiment demonstrates the strong discrimination ability of the mRNA and drug embeddings learned by HGCLMDA, and experiments on sparse data sets showcase the performance and robustness of the method. In-depth analysis of hypergraph structures reveals a crucial role that hypergraphs play in enhancing the performance of models. The case study highlights the potential of HGCLMDA as a valuable tool for predicting mRNA-drug sensitivity associations. The interpretive analysis reveals that HGCLMDA effectively models the similarity between mRNA-mRNA and drug-drug interactions.