Life expectancy has improved with new‐age technologies and advancements in the healthcare sector. Though artificial intelligence (AI) and the Internet of Things (IoT) are revolutionising smart healthcare systems, security of the healthcare data is always a concern. Reversible data hiding (RDH) is widely explored in the healthcare domain for secure data transmission and in areas like cloud computing, satellite image transmission, etc. Medical image transmission plays an important role in the smart health sector. In the case of medical images, a minute error in the reconstructed medical image can mislead the doctor, posing a threat to the patient’s health. Many RDH schemes have been proposed, but very few address from the view of medical images, and that too on high‐quality DICOM images. The proposed AdaBPE RDH scheme is a solution for secure transmission of the patient’s health report (PHR) and other sensitive information with medical specialists. The scheme put forward a technique that maintains a good trade‐off between the smooth pixels for maximum embedding in a block and a lossless recovery. Here, the cover medium employed to hide the patient’s sensitive information is an encrypted 16‐bit DICOM image. The scheme processes the cover image as disjoint blocks of equal size, embedding the information adaptively within the encrypted blocks pertaining to the nature of the actual pixel values in the block through MSB prediction error methodology. The outcomes are evaluated on both the 16‐bit DICOM images and 8‐bit natural images, and the scheme is well poised with RDH goal of BER = 0, PSNR = ∞, and SSIM = 1, achieving an average embedding of 5.7067 bpp on high‐quality medical images and 1.6769 bpp on natural images. The experimental results prove advantageous and are better than other similar state‐of‐the‐art schemes.