Hyperspectral images (HSIs) have recently been exploited in several aspects as HSIs contain many contiguous and narrow discriminative spectral bands. The problem of dimensionality is a significant dilemma for HSIs due to there being plenty of irrelevant and redundant spectral bands and highly correlated bands that lead to Hughes phenomenon. To this end, we present an approach to selecting the most informative and relevant spectral bands for HSI dimensionality reduction using the Krill Herd (KH) algorithm. Moreover, KH is a heuristic search method that seeks to reach the optimum global solution within the search space and effectively evade falling into the local optima. Then an edge-preserving filter was employed to extract the spatial features while reducing noise and obtaining a suitable smoothing that improves the classification performance. Finally, the support vector machine classifier was performed at the pixel level for HSI classification. Furthermore, the proposed work was compared with the harmony search, genetic algorithm, bat algorithm, particle swarm optimization, and firefly algorithm. The experimental results demonstrated outstanding performance with an overall accuracy equal to 96.54%, 98.93%, 99.78%, and 98.66% on four hyperspectral datasets: Indian Pines scene, Pavia University scene, Salinas scene, and Botswana scene, respectively.