Artemisia annua is the plant that produces artemisinin, an endoperoxide-containing sesquiterpenoid used for the treatment of malaria. A. annua extracts, which contain other bioactive compounds, have been used to treat other diseases, including cancer and COVID-19, the disease caused by the virus SARS-CoV-2. In this study, a methyl ester derivative of arteannuin B was isolated when A. annua leaves were extracted with a 1:1 mixture of methanol and dichloromethane. This methyl ester was thought to be formed from the reaction between arteannuin B and the extracting solvent, which was supported by the fact that arteannuin B underwent 1,2-addition when it was dissolved in deuteromethanol. In contrast, in the presence of N-acetylcysteine methyl ester, a 1,4-addition (thiol-Michael reaction) occurred. Arteannuin B hindered the activity of the SARS CoV-2 main protease (nonstructural protein 5, NSP5), a cysteine protease, through time-dependent inhibition. The active site cysteine residue of NSP5 (cysteine-145) formed a covalent bond with arteannuin B as determined by mass spectrometry. In order to determine whether cysteine adduction by arteannuin B can inhibit the development of cancer cells, similar experiments were performed with caspase-8, the cysteine protease enzyme overexpressed in glioblastoma. Time-dependent inhibition and cysteine adduction assays suggested arteannuin B inhibits caspase-8 and adducts to the active site cysteine residue (cysteine-360), respectively. Overall, these results enhance our understanding of how A. annua possesses antiviral and cytotoxic activities.