Essential oils have shown promise as antiviral agents against several pathogenic viruses. In this work we hypothesized that essential oil components may interact with key protein targets of the 2019 severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). A molecular docking analysis was carried out using 171 essential oil components with SARS-CoV-2 main protease (SARS-CoV-2 Mpro), SARS-CoV-2 endoribonucleoase (SARS-CoV-2 Nsp15/NendoU), SARS-CoV-2 ADP-ribose-1″-phosphatase (SARS-CoV-2 ADRP), SARS-CoV-2 RNA-dependent RNA polymerase (SARS-CoV-2 RdRp), the binding domain of the SARS-CoV-2 spike protein (SARS-CoV-2 rS), and human angiotensin−converting enzyme (hACE2). The compound with the best normalized docking score to SARS-CoV-2 Mpro was the sesquiterpene hydrocarbon (E)-β-farnesene. The best docking ligands for SARS−CoV Nsp15/NendoU were (E,E)-α-farnesene, (E)-β-farnesene, and (E,E)−farnesol. (E,E)−Farnesol showed the most exothermic docking to SARS-CoV-2 ADRP. Unfortunately, the docking energies of (E,E)−α-farnesene, (E)-β-farnesene, and (E,E)−farnesol with SARS-CoV-2 targets were relatively weak compared to docking energies with other proteins and are, therefore, unlikely to interact with the virus targets. However, essential oil components may act synergistically, essential oils may potentiate other antiviral agents, or they may provide some relief of COVID-19 symptoms.