In recent years, deep learning has emerged as the dominant approach for hyperspectral image (HSI) classification. However, deep neural networks require large annotated datasets to generalize well. This limits the applicability of deep learning for real-world HSI classification problems, as manual labeling of thousands of pixels per scene is costly and time consuming. In this article, we tackle the problem of few-shot HSI classification by leveraging state-of-the-art self-supervised contrastive learning with an improved view-generation approach. Traditionally, contrastive learning algorithms heavily rely on hand-crafted data augmentations tailored for natural imagery to generate positive pairs. However, these augmentations are not directly applicable to HSIs, limiting the potential of self-supervised learning in the hyperspectral domain. To overcome this limitation, we introduce two positive pair-mining strategies for contrastive learning on HSIs. The proposed strategies mitigate the need for high-quality data augmentations, providing an effective solution for few-shot HSI classification. Through extensive experiments, we show that the proposed approach improves accuracy and label efficiency on four popular HSI classification benchmarks. Furthermore, we conduct a thorough analysis of the impact of data augmentation in contrastive learning, highlighting the advantage of our positive pair-mining approach.