Ergonomic risk assessment is vital for identifying work-related human postures that can be detrimental to the health of a worker. Traditionally, ergonomic risks are reported by human experts through time-consuming and error-prone procedures; however, automatic algorithmic methods have recently started to emerge. To further facilitate the automatic ergonomic risk assessment, this paper proposes a novel variational deep learning architecture to estimate the ergonomic risk of any work-related task by utilizing the Rapid Entire Body Assessment (REBA) framework. The proposed method relies on the processing of RGB images and the extraction of 3D skeletal information that is then fed to a novel deep network for accurate and robust estimation of REBA scores for both individual body parts and the entire body. Through a variational approach, the proposed method processes the skeletal information to construct a descriptive skeletal latent space that can accurately model human postures. Moreover, the proposed method distills knowledge from ground truth ergonomic risk scores and leverages it to further enhance the discrimination ability of the skeletal latent space, leading to improved accuracy. Experiments on two well-known datasets (i.e., University of Washington Indoor Object Manipulation (UW-IOM) and Technische Universität München (TUM) Kitchen) validate the ability of the proposed method to achieve accurate results, overcoming current state-of-the-art methods.