Optimizing the energy consumption of an MEC (Multi-Access Edge Computing) system is a crucial challenge for operation cost reduction and environmental conservation. In this paper, we address an MECS (MEC Server) sleep control problem that aims to reduce the energy consumption of the system while providing users with a reasonable service delay by adjusting the number of active MECSs according to the load imposed on the system. To tackle the problem, we identify two crucial issues that influence the design of an effective sleep control technique and propose methods to address each of these issues. The first issue is accurately predicting the system load. Changes in system load are spatio-temporally correlated among MECSs. By leveraging such correlation information with STGCN (Spatio-Temporal Graph Convolutional Network), we enhance the prediction accuracy of task arrival rates for each MECS. The second issue is rapidly selecting MECSs to sleep when the load distribution over an MEC system is given. The problem of choosing sleep MECS is a combinatorial optimization problem with high time complexity. To address the issue, we employ a genetic algorithm and quickly determine the optimal sleep MECS with the predicted load information for each MECS. Through simulation studies, we verify that compared to the LSTM (Long Short-Term Memory)-based method, our method increases the energy efficiency of an MEC system while providing a compatible service delay.