Reliable uncertainty quantification (UQ) is essential for deploying large language models (LLMs) in safety-critical scenarios, as it enables them to abstain from responding when uncertain, thereby avoiding hallucinations, i.e., plausible yet factually incorrect responses. However, while semantic UQ methods have achieved advanced performance, they overlook latent semantic structural information that could enable more precise uncertainty estimates. In this paper, we propose \underline{Se}mantic \underline{S}tructural \underline{E}ntropy ({SeSE}), a principled black-box UQ framework applicable to both open- and closed-source LLMs. To reveal the intrinsic structure of the semantic space, SeSE constructs its optimal hierarchical abstraction through an encoding tree with minimal structural entropy. The structural entropy of this encoding tree thus quantifies the inherent uncertainty within LLM semantic space after optimal compression. Additionally, unlike existing methods that primarily focus on simple short-form generation, we extent SeSE to provide interpretable, granular uncertainty estimation for long-form outputs. We theoretically prove that SeSE generalizes semantic entropy, the gold standard for UQ in LLMs, and empirically demonstrate its superior performance over strong baselines across 24 model-dataset combinations.