SARS CoV-2 is still considered a global health issue, and its threat keeps growing with the emergence of newly evolved strains. Despite the success in developing some vaccines as a protective measure, finding cost-effective treatments is urgent. Accordingly, we screened a number of phenolic natural compounds for their in vitro anti-SARS CoV-2 activity. We found sinapic acid (SA) selectively inhibited the viral replication in vitro with an half-maximal inhibitory concentration (IC50) value of 2.69 µg/mL with significantly low cytotoxicity (CC50 = 189.3 µg/mL). Subsequently, we virtually screened all currently available molecular targets using a multistep in silico protocol to find out the most probable molecular target that mediates this compound’s antiviral activity. As a result, the viral envelope protein (E-protein) was suggested as the most possible hit for SA. Further in-depth molecular dynamic simulation-based investigation revealed the essential structural features of SA antiviral activity and its binding mode with E-protein. The structural and experimental results presented in this study strongly recommend SA as a promising structural motif for anti-SARS CoV-2 agent development.