Recently, a medical privacy protection scheme (MPPS) based on DNA coding and chaos was proposed in [IEEETrans. Nanobioscience, vol. 16, pp. 850--858, 2017], which uses two coupled chaotic system to generate cryptographic primitives to encrypt color DICOM image. Relying on several statistical experimental results and some theoretical analyses, the designers of MPPS claimed that it is secure against chosen-plaintext attack and the other classic attacks. However, the above conclusion is insufficient without cryptanalysis. In this paper, we first study some properties of MPPS and DNA coding and then propose a chosen-plaintext attack to reveal its equivalent secret-key. It is proved that the attack only needs $lceil log_{256}(3cdot Mcdot N)rceil+4$ chosen plain-images, where $M times N$ is the size of the RGB color image, and ``3 is the number of color channels. Also, the other claimed superiorities are questioned from the viewpoint of modern cryptography. Both theoretical and experimental results are provided to support the feasibility of the attack and the other reported security defects. The proposed cryptanalysis work will promote the proper application of DNA encoding in protecting multimedia data including the DICOM image.