The pandemic disease COVID-19, caused by SARS CoV-2, has created a global crisis. Presently, researchers across the globe are in a quest to identify/develop drugs or vaccines by targeting different non-structural proteins (Nsps) of SARS CoV-2. One such important drug target is Nsp5/main protease (Mpro) which plays a critical role in the viral replication. This cysteine protease/Mpro of SARS CoV-2 has high sequence similarity with the same protease from SARS CoV-1. Previously, it has been shown experimentally that eight polyphenols derived from the root of show inhibitory effect on the cleavage/catalytic activity of the SARS CoV-1 Mpro. But whether these polyphenols exhibit any inhibitory effect on SARS CoV-2 Mpro is unclear. To explore this possibility, here, we have adopted various computational approaches. Polyphenols that qualified the pharmacological parameters (indigo, sinigrin, hesperetin and daidzein) and two well-known Mpro inhibitors (N3 and lopinavir) were subjected to molecular docking studies. Two of them (sinigrin and hesperetin) were selected by comparing their binding affinities with N3 and lopinavir. Sinigrin and hesperetin interacted with the two most important catalytic residues of Mpro (His41 and Cys145). Molecular dynamics studies further revealed that these two Mpro-polyphenol complexes are more stable and experience less conformational fluctuations than Mpro-N3/lopinavir complex. The Mpro-hesperetin complex was more compact and less expanded than Mpro-sinigrin complex. These findings were additionally validated by MM-GBSA analysis. As a whole, our study revealed that these two polyphenols may be potent SARS CoV-2 Mpro inhibitors and may possibly be considered for COVID-19 treatment.