The safety of the passengers and goods in airplanes depends upon a number of combined factors. An airplane's condition and the pilot's experience are pivotal, but another very crucial element is the synchronization among the pilots and the air traffic controller (ATC). The communication link between the two carries many uncertain aspects.  The aviation sector often tends to give more priority to safety rather than cybersecurity.  Although the controller-pilot data communication link (CPDLC) system has been proposed for consistent and reliable communication recently, it has some serious drawbacks. In this paper, we highlight the shortcomings of the CPDLC system from a cyber security perspective. We propose a federated learning-based privacy-preserving intrusion detection system (IDS) to protect the CPDLC from uplink and downlink cyber attacks. To ensure a realistic and viable solution, we created our own training dataset by eavesdropping on the air-ground communication at a site near Arlanda airport, Sweden. The anomaly detection model constructed through federated learning has achieved higher accuracy, precision, recall and F1 score as compared to the centrally and locally trained models, enabling higher security. Due to the lower training loss and time, the proposed approach is highly suitable for the sensitive aviation communications.