Location information serves as the fundamental element for numerous Internet of Things (IoT) applications. Traditional indoor localization techniques often produce significant errors and raise privacy concerns due to centralized data collection. In response, Machine Learning (ML) techniques offer promising solutions by capturing indoor environment variations. However, they typically require central data aggregation, leading to privacy, bandwidth, and server reliability issues. To overcome these challenges, in this paper, we propose a Federated Learning (FL)-based approach for dynamic indoor localization using a Deep Neural Network (DNN) model. Experimental results show that FL has the nearby performance to Centralized Model (CL) while keeping the data privacy, bandwidth efficiency and server reliability. This research demonstrates that our proposed FL approach provides a viable solution for privacy-enhanced indoor localization, paving the way for advancements in secure and efficient indoor localization systems.