The integration of ML in 5G-based Internet of Vehicles (IoV) networks has enabled intelligent transportation and smart traffic management. Nonetheless, the security against adversarial attacks is also increasingly becoming a challenging task. Specifically, Deep Reinforcement Learning (DRL) is one of the widely used ML designs in IoV applications. The standard ML security techniques are not effective in DRL where the algorithm learns to solve sequential decision-making through continuous interaction with the environment, and the environment is time-varying, dynamic, and mobile. In this paper, we propose a Gated Recurrent Unit (GRU)-based federated continual learning (GFCL) anomaly detection framework against adversarial attacks in IoV. The objective is to present a lightweight and scalable framework that learns and detects the illegitimate behavior without having a-priori training dataset consisting of attack samples. We use GRU to predict a future data sequence to analyze and detect illegitimate behavior from vehicles in a federated learning-based distributed manner. We investigate the performance of our framework using real-world vehicle mobility traces. The results demonstrate the effectiveness of our proposed solution for different performance metrics.