Artificial intelligence (AI) has shown promise in detecting and characterizing musculoskeletal diseases from radiographs. However, most existing models remain task-specific, annotation-dependent, and limited in their adaptability across diseases and anatomical regions. Although a comprehensive foundation model trained on large-scale musculoskeletal radiographs is clinically needed, publicly available datasets remain limited in size and lack sufficient diversity to enable training across a wide range of musculoskeletal conditions and anatomical sites. Here, we present SKELEX, a large-scale foundation model for musculoskeletal radiographs, trained using self-supervised learning on 1.2 million diverse, condition-rich images. The model was evaluated on 12 downstream diagnostic tasks and generally outperformed baselines in fracture detection, osteoarthritis grading, and bone tumor classification. Furthermore, SKELEX demonstrated unsupervised reconstruction-based anomaly localization, producing error maps that identified pathologic regions without task-specific training. Building on this capability, we developed an interpretable, region-guided bone tumor classifier. This model maintained robust performance on independent external datasets and was deployed as a publicly accessible web application, serving as a proof of concept for its potential clinical translation. Overall, SKELEX provides a scalable, label-efficient, and broadly applicable AI framework for musculoskeletal radiographs, with its robust external validity specifically demonstrated in bone tumor applications.