CLIP, a foundational vision-language model, has emerged as a powerful tool for open-vocabulary semantic segmentation. While freezing the text encoder preserves its powerful embeddings, recent studies show that fine-tuning both the text and image encoders jointly significantly enhances segmentation performance, especially for classes from open sets. In this work, we explain this phenomenon from the perspective of hierarchical alignment, since during fine-tuning, the hierarchy level of image embeddings shifts from image-level to pixel-level. We achieve this by leveraging hyperbolic space, which naturally encoders hierarchical structures. Our key observation is that, during fine-tuning, the hyperbolic radius of CLIP’s text embeddings decreases, facilitating better alignment with the pixel-level hierarchical structure of visual data. Building on this insight, we propose HyperCLIP, a novel fine-tuning strategy that adjusts the hyperbolic radius of the text embeddings through scaling transformations. By doing so, HyperCLIP equips CLIP with segmentation capability while introducing only a small number of learnable parameters. Our experiments demonstrate that HyperCLIP achieves state-of-the-art performance on open-vocabulary semantic segmentation tasks across three benchmarks, while fine-tuning only approximately 4\% of the total parameters of CLIP. More importantly, we observe that after adjustment, CLIP's text embeddings exhibit a relatively fixed hyperbolic radius across datasets, suggesting that the segmentation task has a characteristic level in hyperbolic space.