Coronavirus disease 2019 (COVID-19) has affected almost every country in the world by causing a global pandemic with a high mortality rate. Lack of an effective vaccine and/or antiviral drugs against SARS-CoV-2, the causative agent, has severely hampered the response to this novel coronavirus. Natural products have long been used in traditional medicines to treat various diseases, and purified phytochemicals from medicinal plants provide a valuable scaffold for the discovery of new drug leads. In the present study, we performed a computational screening of an in-house database composed of ~1000 phytochemicals derived from traditional Saudi medicinal plants with recognised antiviral activity. Structure-based virtual screening was carried out against three druggable SARS-CoV-2 targets, viral RNAdependent RNA polymerase (RdRp), 3-chymotrypsin-like cysteine protease (3CLpro) and papain like protease (PLpro) to identify putative inhibitors that could facilitate the development of potential anti-COVID-19 drug candidates. Computational analyses identified three compounds inhibiting each target, with binding affinity scores ranging from-9.9 to -6.5 kcal/mol. Among these, luteolin 7-rutinoside, chrysophanol 8-(6-galloylglucoside) and kaempferol 7-(6’’-galloylglucoside) bound efficiently to RdRp, while chrysophanol 8-(6galloylglucoside), 3,4,5-tri-O-galloylquinic acid and mulberrofuran G interacted strongly with 3CLpro, and withanolide A, isocodonocarpine and calonysterone bound tightly to PLpro. These potential drug candidates will be subjected to further in vitro and in vivo studies and may assist the development of effective anti-COVID-19 drugs.