Depression is a major global mental health disorder, and the electroencephalogram (EEG) signals have emerged as a promising non-invasive biomarker for its objective assessment. However, the clinical deployment of EEG-based depression detection is hindered by strict privacy regulations, heterogeneous data distributions across institutions, and the impossibility of centralized data integration, resulting in severe data silos and limited model generalizability. To overcome the above-mentioned limitation, we propose a federated domain generalization (FedDG) framework for privacy-preserving EEG-based depression recognition. The framework introduces a fairness-aware global objective that minimizes client-level empirical risk while constraining the variance of generalization gaps across sever domains, thereby promoting consistent cross-domain performance. Furthermore, we develop a generalization adjustment (GA) aggregation strategy that dynamically modulates client weights. The proposed method was evaluated on three publicly EEG depression datasets: MODMA, EDRA, and HUSM, and achieved accuracy rates of 57.76%, 54.14%, and 56.77%, respectively. Experimental results demonstrate that the proposed FedDG framework substantially enhances robustness and generalization to unseen domains while preserving data privacy, offering a viable pathway toward clinically scalable and institution-independent EEG-based depression detection.