A novel strain of coronavirus, namely, SARS-CoV-2 identified in Wuhan city of China in December 2019, continues to spread at a rapid rate worldwide. There are no specific therapies available and investigations regarding the treatment of this disease are still lacking. In order to identify a novel potent inhibitor, we performed blind docking studies on the main virus protease M^pro with eight approved drugs belonging to four pharmacological classes such as: anti-malarial, anti-bacterial, anti-infective and anti-histamine. Among the eight studied compounds, Lymecycline and Mizolastine appear as potential inhibitors of this protease. When docked against M^pro crystal structure, these two compounds revealed a minimum binding energy of −8.87 and −8.71 kcal/mol with 168 and 256 binding modes detected in the binding substrate pocket, respectively. Further, to study the interaction mechanism and conformational dynamics of protein-ligand complexes, Molecular dynamic simulation and MM/PBSA binding free calculations were performed. Our results showed that both Lymecycline and Mizolastine bind in the active site. And exhibited good binding affinities towards target protein. Moreover, the ADMET analysis also indicated drug-likeness properties. Thus it is suggested that the identified compounds can inhibit Chymotrypsin-like protease (3CL^pro) of SARS-CoV-2.