Smart cities aim to improve the quality of life by utilizing technological advancements. One of the main areas of innovation includes the design, implementation, and management of data-intensive medical systems also known as big-data Smart Healthcare systems. Smart health systems need to be supported by highly efficient and resilient security frameworks. One of the important aspects that smart health systems need to provide, is timely access to high-resolution medical images, that form about 80% of the medical data. These images contain sensitive information about the patient and as such need to be secured completely. To prevent unauthorized access to medical images, the process of image encryption has become an imperative task for researchers all over the world. Chaos-based encryption has paved the way for the protection of sensitive data from being altered, modified, or hacked. In this paper, we present an Image Encryption Framework based on Hessenberg transform and Chaotic encryption (IEFHAC), for improving security and reducing computational time while encrypting patient data. IEFHAC uses two 1D-chaotic maps: Logistic map and Sine map for the confusion of data, while diffusion has been achieved by applying the Hessenberg household transform. The Sin and Logistic maps are used to regeneratively affect each other’s output, as such dynamically changing the key parameters. The experimental analysis demonstrates that IEFHAC shows better results like NPCR ranging from 99.66 to 100%, UACI of 37.39%, lesser computational time of 0.36 s, and is more robust to statistical attacks.