Hypergraph contrastive learning enables effective representation learning for hypergraphs without requiring labels. However, existing methods typically rely on randomly deleting or replacing nodes during hypergraph augmentation, which may lead to the absence of critical nodes and further disrupt the higher-order structural relationships within augmented hypergraphs. To address this issue, we propose a Critical Node-aware hypergraph contrastive learning method, which is the first attempt to leverage hyperedge prediction to retain critical nodes and accordingly maintain the reliable higher-order structural relationships within augmented hypergraphs. Specifically, we first employ contrastive learning to align the augmented hypergraphs, and then generate hyperedge embeddings to characterize node representations and their structural correlations. During the hyperedge embedding encoding process, we introduce a hyperedge prediction discriminator to score these embeddings, which quantifies the nodes' contributions to identify the critical nodes and maintain the higher-order structural relationships within augmented hypergraphs. Compared with previous studies, our proposed method can effectively alleviate the erroneous deletion or replacement of critical nodes and steadily maintain the inherent structural relationships between original hypergraph and augmented hypergraphs, naturally guiding better hypergraph representations for downstream tasks. Extensive experiments on various tasks demonstrate that our method is significantly superior to state-of-the-art methods.