Hyperspectral images are rich in spectral and spatial information. However, their high dimensionality and complexity pose significant challenges for effective feature extraction. Specifically, the performance of existing models for hyperspectral image (HSI) classification remains constrained by spectral redundancy among adjacent bands, misclassification at object boundaries, and significant noise in hyperspectral data. To address these challenges, we propose WTCMC—a novel hyperspectral image classification network based on wavelet transform combining Mamba and convolutional neural networks. To establish robust shallow spatial–spectral relationships, we introduce a shallow feature extraction module (SFE) at the initial stage of the network. To enable the comprehensive and efficient capture of both spectral and spatial characteristics, our architecture incorporates a low-frequency spectral Mamba module (LFSM) and a high-frequency multi-scale convolution module (HFMC). The wavelet transform suppresses noise for LFSM and enhances fine spatial and contour features for HFMC. Furthermore, we devise a spectral–spatial complementary fusion module (SCF) that selectively preserves the most discriminative spectral and spatial features. Experimental results demonstrate that the proposed WTCMC network attains overall accuracies (OA) of 98.94%, 98.67%, and 97.50% on the Pavia University (PU), Botswana (BS), and Indian Pines (IP) datasets, respectively, outperforming the compared state-of-the-art methods.