The massive deployment of small cell Base Stations (SBSs) empowered with computing capabilities presents one of the most ingenious solutions adopted for 5G cellular networks towards meeting the foreseen data explosion and the ultra-low latency demanded by mobile applications. This empowerment of SBSs with Multi-access Edge Computing (MEC) has emerged as a tentative solution to overcome the latency demands and bandwidth consumption required by mobile applications at the network edge. The MEC paradigm offers a limited amount of resources to support computation, thus mandating the use of intelligence mechanisms for resource allocation. The use of green energy for powering the network apparatuses (e.g., Base Stations (BSs), MEC servers) has attracted attention towards minimizing the carbon footprint and network operational costs. However, due to their high intermittency and unpredictability, the adoption of learning methods is a requisite. Towards intelligent edge system management, this paper proposes a Green-based Edge Network Management (GENM) algorithm, which is a online edge system management algorithm for enabling green-based load balancing in BSs and energy savings within the MEC server. The main goal is to minimize the overall energy consumption and guarantee the Quality of Service (QoS) within the network. To achieve this, the GENM algorithm performs dynamic management of BSs, autoscaling and reconfiguration of the computing resources, and on/off switching of the fast tunable laser drivers coupled with location-aware traffic scheduling in the MEC server. The obtained simulation results validate our analysis and demonstrate the superior performance of GENM compared to a benchmark algorithm.