We use state-of-the-art computer-aided drug design (CADD) techniques to identify prospective inhibitors of the main protease enzyme, 3CL(pro) of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causing COVID-19. From our screening of over one million compounds including approved drugs, investigational drugs, natural products, and organic compounds, and a rescreening protocol incorporating enzyme dynamics via ensemble docking, we have been able to identify a range of prospective 3CL(pro) inhibitors. Importantly, some of the identified compounds had previously been reported to exhibit inhibitory activities against the 3CL(pro) enzyme of the closely related SARS-CoV virus. The top-ranking compounds are characterized by the presence of multiple bi- and monocyclic rings, many of them being heterocycles and aromatic, which are flexibly linked allowing the ligands to adapt to the geometry of the 3CL(pro) substrate site and involve a high amount of functional groups enabling hydrogen bond formation with surrounding amino acid residues, including the catalytic dyad residues H41 and C145. Among the top binding compounds we identified several tyrosine kinase inhibitors, which include a bioflavonoid, the group of natural products that binds best to 3CL(pro). Another class of compounds that decently binds to the SARS-CoV-2 main protease are steroid hormones, which thus may be endogenous inhibitors and might provide an explanation for the age-dependent severity of COVID-19. Many of the compounds identified by our work show a considerably stronger binding than found for reference compounds with in vitro demonstrated 3CL(pro) inhibition and anticoronavirus activity. The compounds determined in this work thus represent a good starting point for the design of inhibitors of SARS-CoV-2 replication.