This work presents a novel label-efficient self-supervised representation learning-based approach for classifying diabetic retinopathy (DR) images in cross-domain settings. Most of the existing DR image classification methods are based on supervised learning which requires a lot of time-consuming and expensive medical domain experts-annotated data for training. The proposed approach uses the prior learning from the source DR image dataset to classify images drawn from the target datasets. The image representations learned from the unlabeled source domain dataset through contrastive learning are used to classify DR images from the target domain dataset. Moreover, the proposed approach requires a few labeled images to perform successfully on DR image classification tasks in cross-domain settings. The proposed work experiments with four publicly available datasets: EyePACS, APTOS 2019, MESSIDOR-I, and Fundus Images for self-supervised representation learning-based DR image classification in cross-domain settings. The proposed method achieves state-of-the-art results on binary and multi-classification of DR images, even in cross-domain settings. The proposed method outperforms the existing DR image binary and multi-class classification methods proposed in the literature. The proposed method is also validated qualitatively using class activation maps, revealing that the method can learn explainable image representations. The source code and trained models are published on GitHub11https://github.com/prakashchhipa/Learning-Self-Supervised-Representations-for-Label-Efficient-Cross-Domain-Knowledge-Transfer-on-DRF.