There is an urgent necessity of effective medication against severe acute respiratory syndrome coronavirus 2 (SARS CoV-2), which is producing the COVID-19 pandemic across the world. Its main protease (Mpro) represents an attractive pharmacological target due to its involvement in essential viral functions. The crystal structure of free Mpro shows a large structural resemblance with the main protease of SARS CoV (nowadays known as SARS CoV-1). Here, we report that average SARS CoV-2 Mpro is 1900% more sensitive than SARS CoV-1 Mpro in transmitting tiny structural changes across the whole protein through long-range interactions. The largest sensitivity of Mpro to structural perturbations is located exactly around the catalytic site Cys-145 and coincides with the binding site of strong inhibitors. These findings, based on a simplified representation of the protein as a residue network, may help in designing potent inhibitors of SARS CoV-2 Mpro.