To protect the privacy of medical images, as well as the patient personal information associated with it, this paper proposes a reversible data hiding scheme for encrypted medical images; whose reversibility is completely separable by allowing additional data extraction and restoration of the region of interest both from the plaintext and the cipher domain of medical images. To this purpose, the pixels in the image are reordered according to the region of interest selected by the content owner and encrypted with a block cipher in counter mode; to subsequently embed additional data into the encrypted image, such as the patient’s personal information and clinical diagnosis, via less significant bit substitution. Finally, according to the proper key, a legitimate receiver can perform the following tasks: a) Obtain a high visual quality approximate image with respect to the original version by directly decrypting the cryptogram with the encryption key, b) With the data hiding key, the embedded data can be extracted free of any error, either from the encrypted image or its approximate version respectively, and c) In case of having both keys, the embedded data can be extracted and the recovered image with the region of interest fully restored can be obtained without loss of information. The proposed method is suitable for applications where the information security and the management of medical images need to be ensured in terms of reliability, integrity, and confidentiality. Comparison performance with the state of the art is performed, in terms of imperceptibility, capacity and steganalysis.