In light of the inherent entailment relations between images and text, embedding point vectors in hyperbolic space has been employed to leverage its hierarchical modeling advantages for visual semantic representation learning. However, point vector embeddings struggle to address semantic uncertainty, where an image may have multiple interpretations, and text may correspond to different images—a challenge especially prevalent in the medical domain. Therefor, we propose HYDEN, a novel hyperbolic density embedding based image-text representation learning approach tailored for specific medical domain data. This method integrates text-aware local features with global features from images, mapping image-text features to density features in hyperbolic space via using hyperbolic pseudo-Gaussian distributions. An encapsulation loss function is employed to model the partial order relations between image-text density distributions. Experimental results demonstrate the interpretability of our approach and its superior performance compared to the baseline methods across various zero-shot tasks and fine-tuning task on different datasets.