With the advancements in e-healthcare services, it is possible to provide remote medical services to patients and swifter first aid. Medical images play an essential role in e-healthcare applications for providing quick and better remote diagnosis and treatment to patients. Medical images generally comprise secret details about the patients and are therefore prone to various security threats during their transmission over public networks. Thus, it is required to secure these images prior to their communication over public networks. But due to distinctive properties of medical images, like higher correlation and redundancy among the pixels, and larger size, it is required to design an efficient encryption model to resist against various security threats. In this paper, an efficient encryption model for medical images is proposed. To obtain the secret keys, six-dimensional hyperchaotic map (SDHM) is proposed. Firstly, plain medical image is divided into three channels such as red, green, and blue. Secret keys are used to diffuse these channels. Lastly, encrypted channels are concatenated and final encrypted medical image is obtained. Extensive experiments are drawn by considering the benchmark medical images. Also, comparisons are performed among the proposed SDHM and competitive techniques by considering various performance metrics. Comparative analysis reveals that the proposed SDHM achieves remarkably good performance than the existing encryption models.