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Deep Neural Networks (DNNs) methods are widely proposed for cyber security monitoring. However, training DNNs requires a lot of computational resources. This restricts direct deployment of DNNs to resource-constrained environments like the Internet of Things (IoT), especially in federated learning settings that train an algorithm across multiple decentralized edge devices. Therefore, this paper proposes a memory efficient method of training a Fully Connected Neural Network (FCNN) for IoT security monitoring in federated learning settings. The model‘s performance was evaluated against eleven realistic IoT benchmark datasets. Experimental results show that the proposed method can reduce memory requirement by up to 99.46 percentage points when compared to its benchmark counterpart, while maintaining the state-of-the-art accuracy and F1 score.