The growth of digital healthcare has resulted in a significant surge in the creation and sharing of sensitive medical images. Safeguarding the confidentiality and authenticity of these images is paramount to preserve patient privacy and the integrity of healthcare information. In this context, this paper introduces an innovative approach for encrypting medical images by using the principles of the tropical semiring. The tropical semiring is a mathematical framework known for its unique idempotent and tropical arithmetic properties. We utilize the tropical semiring as a basis for establishing a secret key, which is essential for both the encryption and decryption of medical images. The security analysis and the performance analysis of the proposed scheme is given. By employing this method, there is the potential to significantly enhance the security and efficiency of transmitting and storing medical images within the digital healthcare industry.