Unmanned aerial vehicles (UAVs) operating within Flying Ad-hoc Networks (FANETs) encounter security challenges due to the dynamic and distributed nature of these networks. Previous studies focused predominantly on centralized intrusion detection, assuming a central entity responsible for storing and analyzing data from all devices. However, these approaches face challenges including computation and storage costs, along with a single point of failure risk, threatening data privacy and availability. The widespread dispersion of data across interconnected devices underscores the need for decentralized approaches. This paper introduces the Federated Learning-based Intrusion Detection System (FL-IDS), addressing challenges encountered by centralized systems in FANETs. FL-IDS reduces computation and storage costs for both clients and the central server, which is crucial for resource-constrained UAVs. Operating in a decentralized manner, FL-IDS enables UAVs to collaboratively train a global intrusion detection model without sharing raw data, thus avoiding delay in decisions based on collected data, as is often the case with traditional methods. Experimental results demonstrate FL-IDS's competitive performance with Central IDS (C-IDS) while mitigating privacy concerns, with the Bias Towards Specific Clients (BTSC) method further enhancing FL-IDS performance even at lower attacker ratios. Comparative analysis with traditional intrusion detection methods, including Local IDS (L-IDS), sheds light on the strengths of FL-IDS. This study significantly contributes to UAV security by introducing a privacy-aware, decentralized intrusion detection approach tailored to UAV networks. Moreover, by introducing a realistic dataset for FANETs and federated learning, our approach differs from others lacking high dynamism and 3D node movements or accurate federated data federations.