Band selection, which removes irrelevant bands from hyperspectral images (HSIs) and keeps essential spectral information contained in a relatively few bands, allows huge savings in data storage, computation time, and imaging hardware. In this article, we propose a novel structural subspace clustering (STSC) method for hyperspectral band selection, which leverages the self-representation property of data and structural prior information to learn the cluster structure of bands. Particularly, we propose a general clustering model where the coarse coefficients matrix derived from a self-representation model is decomposed as a combination of a desirable coefficients matrix and a sparse matrix. This strategy adaptively adjusts the coarse coefficients matrix to learn the intrinsic data structure in low-dimensional subspaces. To guide this learning process, we introduce a structural regularization approach which makes use of the prior information about local and global properties of spectral bands. Moreover, we incorporate also prior knowledge about the dictionary, which demonstrates to yield a better clustering performance. We develop an adaptive method to estimate the number of selected bands by analyzing eigenvalue gaps of Laplacian matrix. To solve the resulting model, an efficient algorithm based on alternating direction method of multipliers (ADMMs) is developed. Extensive experiments on benchmark HSIs show that our method outperforms the state-of-the-art band selection methods.