The rapid development of Big Data technology supports the advancement of many fields like industrial automation, smart healthcare, distributed systems, and many more. Big data is large and heterogeneous data generated from different sources, such as Internet of Things (IoT) devices, weather forecasting, traffic management systems, etc. However, in a distributed smart healthcare industry, unauthorized users or devices can illegally access healthcare Big Data, as well as control the sensor or IoT-enabled devices connected to a patient's body. They can even alter patients' healthcare Big Data by inserting false and misleading data, which may even cause death to the patient. This study presents a lightweight privacy-preserving user authentication scheme to solve the above-said problems in a distributed smart healthcare system. The proposed scheme prevents unauthorized users from getting access to the healthcare system by establishing a secure session for the authorized user. Here, the password protection mechanism allows only a legitimate user to access and modify the patient's healthcare Big Data. The security strength and effectiveness of the proposed authentication scheme is evaluated in this paper, which show that it is more efficient and secure than the state-of-the-art schemes.