The rapid development of artificial intelligence has driven smart health with next-generation wireless communication technologies, stimulating exciting applications in remote diagnosis and intervention. To enable a timely and effective response for remote healthcare, efficient transmission of medical data through noisy channels with limited bandwidth emerges as a critical challenge. In this work, we propose a novel diffusion-based semantic communication framework, namely DiSC-Med, for the medical image transmission, where medical-enhanced compression and denoising blocks are developed for bandwidth efficiency and robustness, respectively. Unlike conventional pixel-wise communication framework, our proposed DiSC-Med is able to capture the key semantic information and achieve superior reconstruction performance with ultra-high bandwidth efficiency against noisy channels. Extensive experiments on real-world medical datasets validate the effectiveness of our framework, demonstrating its potential for robust and efficient telehealth applications.