The accurate segmentation of remotely sensed hyperspectral images has widespread attention in the Earth observation and remote sensing communities. In the past decade, most of the efforts focus on the development of different supervised methods for hyperspectral image classification. Recently, the computer vision community is developing unsupervised methods that can adapt to new conditions without leveraging expensive supervision. In general, among unsupervised classification methods, sparse subspace clustering (SSC) is a popular tool that achieves good clustering results on experiments with real data. However, for the specific case of hyperspectral clustering, the SSC model does not take into account the spatial information of such images, which limits its discrimination capability and hampering the spatial homogeneity of the clustering results. As a solution, we propose to incorporate a regularization term to the SSC model, which takes into account the neighboring spatial information of spectral pixels in the scene. Specifically, the proposed method uses a three-dimensionall (3D) Gaussian filter to perform a 3D convolution on the sparse coefficients, obtaining a piecewise-smooth representation matrix that enforces an averaging constraint in the SSC optimization program. Extensive simulations demonstrate the effectiveness of the proposed method, achieving an overall accuracy of up to 99% in the selected hyperspectral remote sensing datasets.