The evolution of the wireless sensor network (WSN) in recent years has reached its greatest heights and applications are increasing day by day, one such application is Smart Emergency Monitoring Systems (SMESs) which is in vision of implementation in every urban and rural areas. The implementation of WSN architecture in the Smart Monitoring Systems needs an intelligent scheduling mechanism that efficiently handles the high traffic load as well as the emergency traffic load without sacrificing the energy efficiency of the network. However, the traditional scheduling algorithms such as First Come First Served (FCFS), Round Robin, and Shortest Job First (SJF) cannot meet the requirements of high traffic load in SMESs. To address these shortcomings, this paper presents Emergency Adaptive Medium Access Control protocol (EA-MAC), a fuzzy priority scheduling based Quality-of-service (QoS)-aware medium access control (MAC) protocol for hierarchical WSNs. EA-MAC protocol employs the most powerful fuzzy logics to schedule the sensor nodes with both normal and emergency traffic load without any data congestion, and packet loss and maintaining the better QoS which is considered to be more important in SMESs applications. Moreover, a novel rank-based clustering mechanism in EA-MAC protocol prolongs the network lifetime by minimizing the distance between the Cluster Head (CH) and the Base Station (BS). Both analytical and simulation models demonstrate the superiority of the EA-MAC protocol in terms of energy consumption, transmission delay and data throughput when compared with the existing Time Division Multiple Access (TDMA) based MAC protocols such as LEACH protocol and Cluster Head Election Mechanism-Based On Fuzzy Logic (CHEF) protocol.