Hyperspectral band selection plays a crucial role in reducing the dimensionality of hyperspectral data and enhancing the efficiency of subsequent analysis. However, most methods measure bands using Euclidean distance without considering its limitations in high-dimensional data. In addition, researchers usually select bands based solely on information entropy, without consideration of the impact of noise. To address these challenges, this work introduces a noise-robust hyperspectral band selection model dubbed SSIM-MEMN. The proposed model leverages the structural similarity index (SSIM) to measure the similarity between hyperspectral bands. Additionally, a sorting strategy is devised to identify a representative subset of bands. Specifically, this ranking strategy incorporates both information entropy and noise level to assign scores to individual bands. Consequently, the information pertaining to ground objects is captured with greater precision, leading to enhanced classification accuracy. Extensive experiments were performed to prove the excellent performance of SSIM-MEMN in different sizes of the remaining spectral band subset, and the classification results show that this method is sufficiently robust on different public hyperspectral datasets. In brief, the SSIM-MEMN model provides an effective band selection method for the field of remote sensing image processing and analysis.