Herein, we investigate the structure and flexibility of the hydrated SARS-CoV-2 main protease by means of 2.0 μs molecular dynamics (MD) simulations in explicit solvent. After having performed electrostatic pK_a calculations on several X-ray structures, we consider both the native (unbound) configuration of the enzyme and its noncovalent complex with a model peptide, Ace-Ala-Val-Leu-Gln∼Ser-Nme, which mimics the polyprotein sequence recognized at the active site. For each configuration, we also study their monomeric and homodimeric forms. The simulations of the unbound systems show that the relative orientation of domain III is not stable in the monomeric form and provide further details about interdomain motions, protomer–protomer interactions, inter-residue contacts, accessibility at the catalytic site, etc. In the presence of the peptide substrate, the monomeric protease exhibits a stable interdomain arrangement, but the relative orientation between the scissile peptide bond and the catalytic dyad is not favorable for catalysis. By means of comparative analysis, we further assess the catalytic impact of the enzyme dimerization, the actual flexibility of the active site region, and other structural effects induced by substrate binding. Overall, our computational results complement previous crystallographic studies on the SARS-CoV-2 enzyme and, together with other simulation studies, should contribute to outline useful structure–activity relationships.