The world is still struggling in controlling and containing the spread of the COVID-19 pandemic caused by the SARS-CoV-2 virus. The medical conditions associated with SARS-CoV-2 infections have resulted in a surge in the number of patients at clinics and hospitals, leading to a significantly increased strain on healthcare resources. As such, an important part of managing patients with SARS-CoV-2 infections within the clinical workflow is severity assessment, which is often conducted with the use of chest x-ray (CXR) images. In this work, we introduce COVID-Net CXR-S, a convolutional neural network for predicting the airspace severity of a SARS-CoV-2 positive patient based on a CXR image of the patient's chest. More specifically, we leveraged transfer learning to transfer representational knowledge gained from over 16,000 CXR images from a multinational cohort of over 15,000 patient cases into a custom network architecture for severity assessment. Experimental results with a multi-national patient cohort curated by the Radiological Society of North America (RSNA) RICORD initiative showed that the proposed COVID-Net CXR-S has potential to be a powerful tool for computer-aided severity assessment of CXR images of COVID-19 positive patients. Furthermore, radiologist validation on select cases by two board-certified radiologists with over 10 and 19 years of experience, respectively, showed consistency between radiologist interpretation and critical factors leveraged by COVID-Net CXR-S for severity assessment. While not a production-ready solution, the ultimate goal for the open source release of COVID-Net CXR-S is to act as a catalyst for clinical scientists, machine learning researchers, as well as citizen scientists to develop innovative new clinical decision support solutions for helping clinicians around the world manage the continuing pandemic.