Hyperspectral image (HSI) classification is one of the core tasks in the field of remote sensing, whose key lies in the effective fusion of spectral and spatial information. Among existing methods, convolutional neural networks (CNNs) are limited by their local receptive field, making it difficult to model long-range spectral dependencies, while Transformers, although capable of capturing global relationships, suffer from high quadratic computational complexity. To address these issues, this paper proposes a Multi-scale Cyclic Adaptive Mamba Network (MCAM) based on state-space models (SSM) for hyperspectral image classification. First, a multi-scale feature convolution block is introduced to extract spatial features from local to global levels in parallel, thereby enhancing feature representation. Subsequently, a cyclic adaptive scan module is incorporated to strengthen the modeling of long-range spectral–spatial dependencies. Furthermore, a combination of triplet loss and classification loss is adopted to improve the model’s discriminative ability in few-shot learning scenarios. Experiments conducted on the Indian Pines and Liao Ning-01 datasets demonstrate that MCAM outperforms existing mainstream methods in terms of overall accuracy (OA), average accuracy (AA), and Kappa coefficient, particularly excelling in class boundary clarity and spatial consistency. This study validates the efficiency and potential of the Mamba architecture in HSI classification and provides new insights for subsequent related research.