The novel coronavirus disease 2019 (COVID-19) is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which initially appeared in Wuhan, China, in December 2019. Elderly individuals and those with comorbid conditions may be more vulnerable to this disease. Consequently, several research laboratories continue to focus on developing drugs to treat this infection because this disease has developed into a global pandemic with an extremely limited number of specific treatments available. Natural herbal remedies have long been used to treat illnesses in a variety of cultures. Modern medicine has achieved success due to the effectiveness of traditional medicines, which are derived from medicinal plants. The objective of this study was to determine whether components of natural origin from Iranian medicinal plants have an antiviral effect that can prevent humans from this coronavirus infection using the most reliable molecular docking method; in our case, we focused on the main protease (Mpro) and a receptor-binding domain (RBD). The results of molecular docking showed that among 169 molecules of natural origin from common Iranian medicinal plants, 20 molecules (chelidimerine, rutin, fumariline, catechin gallate, adlumidine, astragalin, somniferine, etc.) can be proposed as inhibitors against this coronavirus based on the binding free energy and type of interactions between these molecules and the studied proteins. Moreover, a molecular dynamics simulation study revealed that the chelidimerine–Mpro and somniferine–RBD complexes were stable for up to 50 ns below 0.5 nm. Our results provide valuable insights into this mechanism, which sheds light on future structure-based designs of high-potency inhibitors for SARS-CoV-2.