The viral main protease (Mpro) from a novel severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) is a key enzyme essential for viral replication and has become an attractive target for antiviral drug development. The Mpro forms a functional dimer and exhibits a pH-dependent enzyme activity and dimerization. Here, we report a molecular dynamics (MD) investigation to gain insights into the structural stability of the enzyme dimer at neutral and acidic pH. Our data shows larger changes in structure of the protein with the acidic pH than that with the neutral pH. Structural analysis of MD trajectories reveals a substantial increase in intersubunit separation, the loss of domain contacts, binding free energy and interaction energy of the dimer which implies the protein instability and tendency of dimer dissociation at acidic pH. The loss in the interaction energy is mainly driven by electrostatic interactions. We have identified the intersubunit hydrogen-bonding residues involved in the decreased dimer stability. These findings may be helpful for rational drug design and target evaluation against COVID-19.