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Recently, anomaly detection and localization in multimedia data have received significant attention among the machine learning community. In real-world applications such as medical diagnosis and industrial defect detection, anomalies only present in a fraction of the images. To extend the reconstruction-based anomaly detection architecture to the localized anomalies, we propose a self-supervised learning approach through random masking and then restoring, named Self-Supervised Masking (SSM) for unsupervised anomaly detection and localization. SSM not only enhances the training of the inpainting network but also leads to great improvement in the efficiency of mask prediction at inference. Through random masking, each image is augmented into a diverse set of training triplets, thus enabling the autoencoder to learn to reconstruct with masks of various sizes and shapes during training. To improve the efficiency and effectiveness of anomaly detection and localization at inference, we propose a novel progressive mask refinement approach that progressively uncovers the normal regions and finally locates the anomalous regions. The proposed SSM method outperforms several state-of-the-arts for both anomaly detection and anomaly localization, achieving 98.3% AUC on Retinal-OCT and 93.9% AUC on MVTec AD, respectively.