With the explosive growth of the Internet of Things (IoT) devices deployed in edge networks, the functionalities of IoT devices are typically encapsulated as IoT services, and user requests can be achieved through the composition of data and/or computation-intensive IoT services. Considering the prediction-uncertainty of forthcoming requests, certain IoT services may (i) not be hosted currently by appropriate IoT devices, or (ii) such an IoT service exists, but its non-functional properties may hardly be satisfied with respect to certain constraints prescribed by requests. To address this challenge, this paper proposes an efficiency-aware service Migration Scheduling (denoted eMS) mechanism in edge networks, in order to migrate IoT services on-demand, and thus, to optimally settle non-satisfiable constraints. Specifically, IoT services are re-scheduled, such that certain IoT services are migrated from their hosting IoT devices to neighboring ones, while minimizing the energy consumption and average delay caused by this service re-scheduling operation. We formulate this service re-scheduling as a multi-objective and multi-constraint optimization problem, which is solved through integrating the greedy algorithm into the fast non-dominated sorting and crowded-comparison operators as the hybrid genetic algorithm (G-NSGA-II). Based on real-life datasets provided by an oil pipeline monitoring project, extensive experiments are conducted, and evaluation results show that our eMS is promising in reducing the energy consumption and average delay of service re-scheduling in comparison with the state-of-art’s techniques.