Hyperspectral image classification often requires selecting the most informative bands instead of processing the whole data without losing the geometrical representation of the data. Existing dimensionality reduction and band selection methods have the capability to reveal the nonlinear properties exhibited in the data but at the expense of losing its geometrical representation. To cope with the said issue, an unsupervised nonlinear deep autoencoder (UDAE) based band selection method is proposed. Our aim is to find an optimal mapping and construct a lower-dimensional space that has a similar structure to the original data with least reconstruction error. Our experiments on a publicly available hyperspectral dataset, with various types of classifiers, demonstrate the effectiveness of UDAE method, which equates favorably with other state-of-the-art dimensionality reduction and band selection methods.