Deep reinforcement learning algorithms (DRL) are increasingly being used in safety-critical systems. Ensuring the safety of DRL agents is a critical concern in such contexts. However, relying solely on testing is not sufficient to ensure safety as it does not offer guarantees. Building safety monitors is one solution to alleviate this challenge. This paper proposes SMARLA, a machine learning-based safety monitoring approach designed for DRL agents. For practical reasons, SMARLA is designed to be black-box (as it does not require access to the internals of the agent) and leverages state abstraction to reduce the state space and thus facilitate the learning of safety violation prediction models from agent’s states. We validated SMARLA on two well-known RL case studies. Empirical analysis reveals that SMARLA achieves accurate violation prediction with a low false positive rate, and can predict safety violations at an early stage, approximately halfway through the agent’s execution before violations occur.