Multi-cloud computing is no different than other Cloud computing (CC) models when it comes to providing users with self-services IT resources. For instance, a company can use services of one specific cloud Service Provider (CSP) for its business, as it can use more than one CSP either to get the best of each without any vendor lock-in. However, the situation is different regarding monitoring a multi-cloud environment. In fact, CSPs provide in-house monitoring tools that are natively compatible with their environment but lack support for other CSP's environments, which is problematic for any company that wants to use more than a CSP. In addition, third party cloud monitoring tools often use agents installed on each monitored virtual machine (VM) to collect monitoring data and send them to a central monitoring server that is hosted on premise or on a Cloud, which increases bottlenecks and latency while transmitting data or processing it. Therefore, this paper presents a monitoring framework for multi-cloud environments that implements edge computing and RESTFul microservices for a high efficiency monitoring and scalability. In fact, the monitoring framework "EMMCS" uses SNMP agents to collect metrics, and performs all monitoring tasks at the edge of each cloud to enhance network transmission and data processing at the central monitoring server level. The implementation of the framework is tested on different public cloud environments, namely Amazon AWS and Microsoft Azure to show the efficiency of the proposed approach.