Reversible data hiding (RDH) into encrypted images is of increasing attention to researchers as the original content can be perfectly reconstructed after the embedded data are extracted while the content owner’s privacy remains protected. The existing RDH techniques are designed for grayscale images and, therefore, cannot be directly applied to palette images. Since the pixel values in a palette image are not the actual color values, but rather the color indexes, RDH in encrypted palette images is more challenging than that designed for normal image formats. To the best knowledge of the authors, there is no suitable RDH scheme designed for encrypted palette images that has been reported, while palette images have been widely utilized. This has motivated us to design a reliable RDH scheme for encrypted palette images. The proposed method adopts a color partitioning method to use the palette colors to construct a certain number of embeddable color triples, whose indexes are self-embedded into the encrypted image so that a data hider can collect the usable color triples to embed the secret data. For a receiver, the embedded color triples can be determined by verifying a self-embedded check code that enables the receiver to retrieve the embedded data only with the data hiding key. Using the encryption key, the receiver can roughly reconstruct the image content. Experiments have shown that our proposed method has the property that the presented data extraction and image recovery are separable and reversible. Compared with the state-of-the-art works, our proposed method can provide a relatively high data-embedding payload, maintain high peak signal-to-noise ratio values of the decrypted and marked images, and have a low computational complexity.