We present IntrinsicAvatar, a novel approach to recovering the intrinsic properties of clothed human avatars including geometry, albedo, material, and environment lighting from only monocular videos. Recent advancements in human-based neural rendering have enabled high-quality geometry and appearance reconstruction of clothed humans from just monocular videos. However, these methods bake intrinsic properties such as albedo, material, and environment lighting into a single entangled neural representation. On the other hand, only a handful of works tackle the problem of estimating geometry and disentangled appearance properties of clothed humans from monocular videos. They usually achieve limited quality and disentanglement due to approximations of secondary shading effects via learned MLPs. In this work, we propose to model secondary shading effects explicitly via Monte-Carlo ray tracing. We model the rendering process of clothed humans as a volumetric scattering process, and combine ray tracing with body articulation, essentially tracing secondary rays through the canonical space that represents geometry and appearance. Our approach can recover high-quality geometry, albedo, material, and lighting properties of clothed humans from a single monocular video, without requiring supervised pre-training using ground truth materials which are hard to obtain in practice. Furthermore, since we explicitly model the volumetric scattering process and ray tracing, our model naturally generalizes to novel poses, enabling animation of the reconstructed avatar in novel lighting conditions.