To address the low hyperspectral image (HSI) pixel classification accuracy caused by few number of labeled training samples and high-dimensional spectral data, this study proposes a self-supervised learning-based feature extraction method to extract low-dimensional features representing crucial information of HSI data. First, an unsupervised data augmentation was used to expand the HSI training dataset. Then, the feature extraction module constructed by an external attention module was trained using an extended training dataset under a self-supervised framework. The self-affinity features between bands of a single sample and the potential correlation between different samples were extracted under the supervision of the intrinsic co-occurrence attributes of the spectral data. Finally, the trained feature extraction module was applied to reduce the dimension of raw HSI data, and the low-dimensional features were input to the subsequent classifier to classify the HSI pixels. The feasibility and effectiveness of the proposed method were evaluated through quantitative evaluation of dimensionality reduction results on Indian Pines, Salinas, and Pavia University datasets. The experimental results show that the feature extraction module generated using the proposed method can fully extract the spatial-spectral features from the original spectra. The proposed method is insensitive to the size of the training set and is suitable for small-sized HSI data.