Federated learning (FL) has become an emerging machine learning technique lately due to its efficacy in safeguarding the client's confidential information. Nevertheless, despite the inherent and additional privacy-preserving mechanisms (e.g., differential privacy, secure multi-party computation, etc.), the FL models are still vulnerable to various privacy-violating and security-compromising attacks (e.g., data or model poisoning) due to their numerous attack vectors which in turn, make the models either ineffective or sub-optimal. Existing adversarial models focusing on untargeted model poisoning attacks are not enough stealthy and persistent at the same time because of their conflicting nature (large scale attacks are easier to detect and vice versa) and thus, remain an unsolved research problem in this adversarial learning paradigm. Considering this, in this paper, we analyze this adversarial learning process in an FL setting and show that a stealthy and persistent model poisoning attack can be conducted exploiting the differential noise. More specifically, we develop an unprecedented DP-exploited stealthy model poisoning (DeSMP) attack for FL models. Our empirical analysis on both the classification and regression tasks using two popular datasets reflects the effectiveness of the proposed DeSMP attack. Moreover, we develop a novel reinforcement learning (RL)-based defense strategy against such model poisoning attacks which can intelligently and dynamically select the privacy level of the FL models to minimize the DeSMP attack surface and facilitate the attack detection.