Depression detection using deep learning models has been widely explored in previous studies, especially due to the large amounts of data available from social media posts. These posts provide valuable information about individuals' mental health conditions and can be leveraged to train models and identify patterns in the data. However, distributed learning approaches have not been extensively explored in this domain. In this study, we adopt Federated Learning (FL) to facilitate decentralized training on smartphones while protecting user data privacy. We train three neural network architectures--GRU, RNN, and LSTM on Reddit posts to detect signs of depression and evaluate their performance under heterogeneous FL settings. To optimize the training process, we leverage a common tokenizer across all client devices, which reduces the computational load. Additionally, we analyze resource consumption and communication costs on smartphones to assess their impact in a real-world FL environment. Our experimental results demonstrate that the federated models achieve comparable performance to the centralized models. This study highlights the potential of FL for decentralized mental health prediction by providing a secure and efficient model training process on edge devices.