The irreversible inhibition of the main protease of SARS-CoV-2 by a Michael acceptor compound known as N3 has been investigated using multiscale simulation methods. The noncovalent enzyme-inhibitor complex was simulated using classical Molecular Dynamics techniques and the pose of the inhibitor in the active site was compared to that of the natural substrate, a peptide containing the Gln-Ser scissile bond. The formation of the covalent enzyme-inhibitor complex was then simulated using hybrid QM/MM free energy methods. After binding, the reaction mechanism was found to be composed of two steps: i) the activation of the catalytic dyad (Cys145 and His41) to form an ion pair and ii) a Michael addition where the attack of the Sg atom of Cys145 to the Cb atom of the inhibitor precedes the water-mediated proton transfer from His41 to the Ca atom. The microscopic description of protease inhibition by N3 obtained from our simulations is strongly supported by the excellent agreement between the estimated activation free energy and the value derived from kinetic experiments. Comparison with the acylation reaction of a peptide substrate suggest that that N3-based inhibitors could be improving adding chemical modifications that could facilitate the formation of the catalytic dyad ion pair.