The integration of medical signal processing capabilities and advanced sensors into Internet of Things (IoT) devices plays a key role in providing comfort and convenience to human lives. As the number of patients is increasing gradually, providing healthcare facilities to each patient, particularly to the patients located in remote regions, not only has become challenging but also results in several issues, such as: (i) increase in workload on paramedics, (ii) wastage of time, and (iii) accommodation of patients. Therefore, the design of smart healthcare systems has become an important area of research to overcome these above-mentioned issues. Several healthcare applications have been designed using wireless sensor networks (WSNs), cloud computing, and fog computing. Most of the e-healthcare applications are designed using the cloud computing paradigm. Cloud-based architecture introduces high latency while processing huge amounts of data, thus restricting the large-scale implementation of latency-sensitive e-healthcare applications. Fog computing architecture offers processing and storage resources near to the edge of the network, thus, designing e-healthcare applications using the fog computing paradigm is of interest to meet the low latency requirement of such applications. Patients that are minors or are in intensive care units (ICUs) are unable to self-report their pain conditions. The remote healthcare monitoring applications deploy IoT devices with bio-sensors capable of sensing surface electromyogram (sEMG) and electrocardiogram (ECG) signals to monitor the pain condition of such patients. In this article, fog computing architecture is proposed for deploying a remote pain monitoring system. The key motivation for adopting the fog paradigm in our proposed approach is to reduce latency and network consumption. To validate the effectiveness of the proposed approach in minimizing delay and network utilization, simulations were carried out in iFogSim and the results were compared with the cloud-based systems. The results of the simulations carried out in this research indicate that a reduction in both latency and network consumption can be achieved by adopting the proposed approach for implementing a remote pain monitoring system.