Reactive injection attacks are a class of security threats in wireless networks wherein adversaries opportunistically inject spoofing packets in the frequency band of a client thereby forcing the base-station to deploy impersonation-detection methods. Towards circumventing such threats, we implement secret-key based physical-layer signalling methods at the clients which allow the base-stations to deploy machine learning (ML) models on their in-phase and quadrature samples at the baseband for attack detection. Using Adalm Pluto based software defined radios to implement the secret-key based signalling methods, we show that robust ML models can be designed at the base-stations. However, we also point out that, in practice, insufficient availability of training datasets at the base-stations can make these methods ineffective. Thus, we use a federated learning framework in the backhaul network, wherein a group of base-stations that need to protect their clients against reactive injection threats collaborate to refine their ML models by ensuring privacy on their datasets. Using a network of XBee devices to implement the backhaul network, experimental results on our federated learning setup shows significant enhancements in the detection accuracy, thus presenting wireless security as an excellent use-case for federated learning in 6G networks and beyond.