Deep learning (DL) methodology contributes a lot to the development of hyperspectral image (HSI) analysis community. However, it also makes HSI analysis systems vulnerable to adversarial attacks. To this end, we propose a masked spatial-spectral autoencoder (MSSA) in this article under self-supervised learning theory, for enhancing the robustness of HSI analysis systems. First, a masked sequence attention learning (MSAL) module is conducted to promote the inherent robustness of HSI analysis systems along spectral channel. Then, we develop a graph convolutional network (GCN) with learnable graph structure to establish global pixel-wise combinations. In this way, the attack effect would be dispersed by all the related pixels among each combination, and a better defense performance is achievable in spatial aspect. Finally, to improve the defense transferability and address the problem of limited labeled samples, MSSA employs spectra reconstruction as a pretext task and fits the datasets in a self-supervised manner. Comprehensive experiments over three benchmarks verify the effectiveness of MSSA in comparison with the state-of-the-art hyperspectral classification methods and representative adversarial defense strategies.