Contactless diagnosis of musculoskeletal disorders can potentially improve population health as well as robot behaviours in collaborative settings. However, current diagnosis methods require an in-person physical examination in which a trained physician senses, through contact, the force applied by various muscles. Simulation tools exist, but their use for diagnosis with real data is under-explored. In this paper, we propose an algorithm for identifying which upper-limb muscle group is fatigued. Our algorithm compares the realworld free-space motion of the subject with that of a simulated musculoskeletal model, and is therefore contactless: preventing the need for invasive sensing or in-person assessment. Our algorithm simulates various fatigue conditions using a physics-based musculoskeletal model and extracts diagnostic motion features from both real and simulated data, which are compared for diagnosis. Experimental results on real data demonstrate that the proposed method can reliably distinguish between multiple muscle-groups of fatigue. Additionally, through comprehensive performance comparisons, we show how recent advanced musculoskeletal simulators can be properly configured to address the sim-to-real gap in the context of the fatigue diagnosis task. Our approach can potentially spur further research in remote and automated diagnosis, significantly lowering the barrier to large-scale and early detection.