Modern communication networks like 5G and 6G are characterized by unpredictable traffic patterns and dynamic communication network characteristics. This makes network management a particularly challenging task. To address this problem, various Machine Learning approaches have been investigated. Moreover, with the increasing integration of Distributed Machine Learning solutions for the emerging mobile communication networks to achieve fast decision-making operations, network management services are accommodating this paradigm shift to ensure decentralized management operations. In this paper, we address the problem of end-to-end latency minimization in complex communication networks like 5G and future 6G networks. To achieve this goal, we propose a Multi-Agent Deep Reinforcement Learning approach to minimize end-to-end latency by adopting a reward-based dynamic multi-path routing strategy. The preliminary evaluation results show that our solution presents a good performance compared to a naive approach (i.e.; ML-free routing) when considering different traffic patterns.