Eucalyptus essential oils are well-known and used especially in upper respiratory tract pathologies or diseases as herbal drug preparations. In the present study, the in vitro angiotensin-converting enzyme 2 (ACE2) and lipoxygenase (LOX) enzyme inhibitory potentials of commercial Eucalyptus globulus Labill. and Eucalyptus citriodora Hook. essential oils were evaluated for their potential anti-coronavirus disease 2019 (COVID-19), and anti-inflammatory effects. In addition, the major components, 1,8-cineole and citronellal, were evaluated for their ability to bind at the active site of either human ACE2 or human 5-LOX using an in silico setting. Before activity evaluation, Eucalyptus globulus and E citriodora essential oils were analysed by GC/FID and GC/MS, where 1,8-cineole (30%), and citronellal (80%) were identified as the major components, respectively. The in vitro ACE2 inhibition was calculated as 94.9% for E globulus, and that of E citriodora essential oil as 83.4%. In vitro LOX inhibition experiments for essential oils in the same order showed inhibitions of 71.3 and 91.4%, respectively, at 20 µg/mL test concentrations in microplate-based fluorometric assays. In addition, protein–ligand docking, and interaction profiling was used to gain structural and mechanistic insights into the in silico ACE2 and LOX inhibitory potentials of the major Eucalyptus essential oil constituents, 1,8-cineole as well as citronellal. The resulting data supported the in vitro findings; however, further in vivo studies are needed to confirm the activity.