Unsupervised segmentation of hyperspectral images is an important problem in the field of image processing with many applications, including scene labelling of remote-sensing images and object detection in medical images. However, the high-dimensionality of hyperspectral images poses considerable challenges in this problem. In previous studies, to deal with high-dimensionality, band selection has been performed as a separate step before image segmentation. In this approach, however, information loss can occur because band selection methods do not consider the segmentation task when they select the bands. In addition, in most segmentation tasks, the fact that the number of segments of the image needs to be given before the segmentation task is also an issue. To address these challenges, we propose a method for simultaneous segmentation of hyperspectral images and selection of important bands that are highly involved in the segmentation task. The proposed method, called a mixture of finite maximum margin mixtures, combines a mixture of finite mixtures, which allows the number of segments to be automatically inferred from the data, and a maximum margin classifier, which allows a flexible segmentation and tractable inference on the segmentation labels. Furthermore, we simultaneously select useful bands that help with the segmentation during the segmentation procedure by introducing a latent binary vector that represents discriminating or non-discriminating bands. We demonstrate the advantages of the proposed method using four real datasets.