Parkinson's disease (PD) is a progressive neurological disorder primarily affecting motor function resulting in tremor at rest, rigidity, bradykinesia, and postural instability. The physical severity of PD impairments can be quantified through the Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS), a widely used clinical rating scale. Accurate and quantitative assessment of disease progression is critical to developing a treatment that slows or stops further advancement of the disease. Prior work has mainly focused on dopamine transport neuroimaging for diagnosis or costly and intrusive wearables evaluating motor impairments. For the first time, we propose a computer vision-based model that observes non-intrusive video recordings of individuals, extracts their 3D body skeletons, tracks them through time, and classifies the movements according to the MDS-UPDRS gait scores. Experimental results show that our proposed method performs significantly better than chance and competing methods with an F1-score of 0.83 and a balanced accuracy of 81%. This is the first benchmark for classifying PD patients based on MDS-UPDRS gait severity and could be an objective biomarker for disease severity. Our work demonstrates how computer-assisted technologies can be used to non-intrusively monitor patients and their motor impairments. The code is available at https://github.com/mlu355/PD-Motor-Severity-Estimation.