Cross-modal retrieval struggles with modeling hierarchical structures and distinguishing hard negative samples in multi-modal data using traditional Euclidean space. This paper introduces Hierarchical Hyperbolic Contrastive Learning (HHCL), a novel framework embedding multimodal features into a shared hyperbolic space to overcome these issues. HHCL leverages multimodal encoders and hyperbolic projection layers to map features onto the Poincaré ball model. Its core innovation is an adaptive curvature hyperbolic contrastive loss, dynamically learning and optimizing curvature parameters based on local data characteristics. This captures multi-scale hierarchical information and addresses hard negative samples. Evaluated on fine-grained crossmodal retrieval tasks across MS-COCO, Flickr30K, and a CUB-200-2011 subset, HHCL consistently achieves state-of-the-art performance, significantly outperforming Euclidean baselines and fixed-curvature hyperbolic approaches. Ablation studies validate the adaptive curvature's effectiveness. Qualitative analyses demonstrate HHCL's superior ability to align fine-grained semantic details, positioning it as a robust solution for complex cross-modal matching.