Deep Learning (DL) has been widely proposed for botnet attack detection in Internet of Things (IoT) networks. However, the traditional Centralized DL (CDL) method cannot be used to detect previously unknown (zero-day) botnet attack without breaching the data privacy rights of the users. In this paper, we propose Federated Deep Learning (FDL) method for zero-day botnet attack detection to avoid data privacy leakage in IoT edge devices. In this method, an optimal Deep Neural Network (DNN) architecture is employed for network traffic classification. A model parameter server remotely coordinates the independent training of the DNN models in multiple IoT edge devices, while Federated Averaging (FedAvg) algorithm is used to aggregate local model updates. A global DNN model is produced after a number of communication rounds between the model parameter server and the IoT edge devices. Zero-day botnet attack scenarios in IoT edge devices is simulated with the Bot-IoT and N-BaIoT data sets. Experiment results show that FDL model: (a) detects zero-day botnet attacks with high classification performance; (b) guarantees data privacy and security; (c) has low communication overhead (d) requires low memory space for the storage of training data; and (e) has low network latency. Therefore, FDL method outperformed CDL, Localized DL, and Distributed DL methods in this application scenario. Index Terms-Cybersecurity, botnet detection, federated learning, deep learning, deep neural network, Internet of Things. I. INTRODUCTION B OTNET attack is a serious cyber security challenge facing the Internet of Things (IoT) [1]-[3]. In our context, a botnet is a network of compromised devices that is used to launch cyber attack against critical infrastructures [4]. This cyber attack may be in form of Denial of Service (DoS), Distributed DoS (DDoS), reconnaissance, or data theft [5].