Internet of Things (IoT) and cyber‐physical systems demand proper real‐time data processing and analysis to fulfill the essential characteristics of seamless computing services such as less processing time, dynamic network management, and location awareness. With the evolution of mobile edge computing, numerous security and privacy issues have been addressed including policy management, authentication, access control, and confidentiality. The technologies such as big‐data, Internet of Things, and cloud have improved the development of modern healthcare systems to improve the quality of medical services. It is nowadays integrating the computing methods and communication technologies such as wireless sensor networks, radio frequency identification, smartphones, and location awareness to collect and analyze the physiological data of the patient. The e‐Health entities such as medical device, client, and server rely on analytical models to carry out early diagnosis and remote monitoring. As it is based on e‐Health applications, a real‐time healthcare system is preferred to integrate with mobile cloud computing. Since the medical data are hugely exposed to vulnerabilities, a lightweight privacy‐aware secure authentication (LPASA) scheme is presented. To achieve better secure efficiencies, this article is preferable to use lightweight cryptographic operations, namely, one‐way hashing function and bitwise exclusive‐OR. Moreover, the formal and informal security analysis shows that the proposed LPASA can withstand the possible active and passive attacks such as replay, man‐in‐the‐middle, privileged‐insider, online‐guessing, and so forth. The experimental analysis demonstrates that the proposed LPASA scheme achieves a better quality of services in terms of packet delivery ratio, energy consumption per data delivery bit, and percentage of packets with low latency to adopt in resource‐constrained environments.