The Audio-Visual Question Answering (AVQA) task holds significant potential for applications. Compared to traditional unimodal approaches, the multi-modal input of AVQA makes feature extraction and fusion processes more challenging. Euclidean space is difficult to effectively represent multi-dimensional relationships of data. Especially when extracting and processing data with a tree structure or hierarchical structure, Euclidean space is not suitable as an embedding space. Additionally, the self-attention mechanism in Transformers is effective in capturing the dynamic relationships between elements in a sequence. However, the self-attention mechanism's limitations in window modeling and quadratic computational complexity reduce its effectiveness in modeling long sequences. To address these limitations, we propose SHMamba: Structured Hyperbolic State Space Model to integrate the advantages of hyperbolic geometry and state space models. Specifically, SHMamba leverages the intrinsic properties of hyperbolic space to represent hierarchical structures and complex relationships in audio-visual data. Meanwhile, the state space model captures dynamic changes over time by globally modeling the entire sequence. Furthermore, we introduce an adaptive curvature hyperbolic alignment module and a cross fusion block to enhance the understanding of hierarchical structures and the dynamic exchange of cross-modal information, respectively. Extensive experiments demonstrate that SHMamba outperforms previous methods with fewer parameters and computational costs. Our learnable parameters are reduced by 78.12\%, while the average performance improves by 2.53\%. Experiments show that our method demonstrates superiority among all current major methods and is more suitable for practical application scenarios.