Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was found to be a severe threat to global public health in late 2019. Nevertheless, no approved medicines have been found to inhibit the virus effectively. Anti-malarial and antiviral medicines have been reported to target the SARS-CoV-2 virus. This paper chose eight natural eucalyptus compounds to study their binding interactions with the SARS-CoV-2 main protease (Mpro) to assess their potential for becoming herbal drugs for the new SARS-CoV-2 infection virus. In-silico methods such as molecular docking, molecular dynamics (MD) simulations, and Molecular Mechanics Poisson Boltzmann Surface Area (MM/PBSA) analysis were used to examine interactions at the atomistic level. The results of molecular docking indicate that Mpro has good binding energy for all compounds studied. Three docked compounds, α-gurjunene, aromadendrene, and allo-aromadendrene, with highest binding energies of −7.34 kcal/mol (−30.75 kJ/mol), −7.23 kcal/mol (−30.25 kJ/mol), and −7.17 kcal/mol (−29.99 kJ/mol) respectively, were simulated with GROningen MAchine for Chemical Simulations (GROMACS) to measure the molecular interactions between Mpro and inhibitors in detail. Our MD simulation results show that α-gurjunene has the strongest binding energy of −20.37 kcal/mol (−85.21 kJ/mol), followed by aromadendrene with −18.99 kcal/mol (−79.45 kJ/mol), and finally allo-aromadendrene with −17.91 kcal/mol (−74.95 kJ/mol). The findings indicate that eucalyptus may be used to inhibit the Mpro enzyme as a drug candidate. This is the first computational analysis that gives an insight into the potential role of structural flexibility during interactions with eucalyptus compounds. It also sheds light on the structural design of new herbal medicinal products against Mpro.