AI-based semantic and instance segmentation of terrestrial and drone LiDAR point clouds is emerging as a transformative approach for converting the complex 3D structure of forests into actionable information for forest monitoring and biodiversity assessment. However, forest LiDAR scenes remain highly challenging due to their large data volumes, irregular sampling density, overlapping and complex canopy structure, and geographic variability. Existing methods based on sparse convolutions or Transformers achieve promising results, but suffer from two key limitations: Quadratic complexity of attention scales poorly to large forest scenes, and Generic context modeling does not exploit forest structural priors, limiting tree separation in complex regions. To address these challenges, we propose ForestMamba, a structure-aware method that incorporates forest-specific priors into feature encoding, query generation, and query refinement, while replacing quadratic attention with linear-time state-space modeling. First, we introduce a sparse encoder with vertical-priority slab serialization that organizes sparse voxels into vertically coherent sequences for efficient long-range context modeling. Second, we propose a geometry-guided query initialization strategy based on an on-the-fly multi-scale Canopy Height Model (CHM), where canopy maxima provide ecologically meaningful query seeds, supplemented by Farthest Point Sampling (FPS) to cover understory trees. Third, we design a Mamba-based query decoder that combines local kNN voxel aggregation with a spatial dual-path Mamba for query refinement with linear computational complexity. Extensive experiments across seven forest regions demonstrate that ForestMamba consistently outperforms existing baselines in both segmentation tasks, while achieving 3 times faster inference and 2.3 times lower GPU memory than Transformer-based methods.