Background: SARS-CoV-2 is the causal agent of the current coronavirus disease 2019 (COVID-19) pandemic. They are enveloped, positive-sense, single-stranded RNA viruses of the Coronaviridae family. Proteases of SARS-CoV-2 are necessary for viral replication, structural assembly, and pathogenicity. The approximately 33.8 kDa M^pro protease of SARS-CoV-2 is a non-human homologue and is highly conserved among several coronaviruses, indicating that M^pro could be a potential drug target for Coronaviruses. Methods: Herein, we performed computational ligand screening of four pharmacophores (OEW, remdesivir, hydroxychloroquine and N3) that are presumed to have positive effects against SARS-CoV-2 M^pro protease (6LU7), and also screened 50,000 natural compounds from the ZINC Database dataset against this protease target. Results: We found 40 pharmacophore-like structures of natural compounds from diverse chemical classes that exhibited better affinity of docking as compared to the known ligands. The 11 best selected ligands, namely ZINC1845382, ZINC1875405, ZINC2092396, ZINC2104424, ZINC44018332, ZINC2101723, ZINC2094526, ZINC2094304, ZINC2104482, ZINC3984030, and ZINC1531664, are mainly classified as beta-carboline, alkaloids, and polyflavonoids, and all displayed interactions with dyad CYS145 and HIS41 from the protease pocket in a similar way as other known ligands. Conclusions: Our results suggest that these 11 molecules could be effective against SARS-CoV-2 protease and may be subsequently tested in vitro and in vivo to develop novel drugs against this virus.