The novel coronavirus, SARS-CoV-2, has caused a recent pandemic called COVID-19 and a severe health threat around the world. In the current situation, the virus is rapidly spreading worldwide, and the discovery of a vaccine and potential therapeutics are critically essential. The crystal structure for the main protease (Mpro) of SARS-CoV-2, 3-chymotrypsin-like cysteine protease (3CLpro), was recently made available and is considerably similar to the previously reported SARS-CoV. Due to its essentiality in viral replication, it represents a potential drug target. Herein, a computer-aided drug design (CADD) approach was implemented for the initial screening of 13 approved antiviral drugs. Molecular docking of 13 antivirals against the 3-chymotrypsin-like cysteine protease (3CLpro) enzyme was accomplished, and indinavir was described as a lead drug with a docking score of -8.824 and a XP Gscore of -9.466 kcal/mol. Indinavir possesses an important pharmacophore, hydroxyethylamine (HEA), and thus, a new library of HEA compounds (>2500) was subjected to virtual screening that led to 25 hits with a docking score more than indinavir. Exclusively, compound 16 with a docking score of -8.955 adhered to drug-like parameters, and the structure-activity relationship (SAR) analysis was demonstrated to highlight the importance of chemical scaffolds therein. Molecular dynamics (MD) simulation analysis performed at 100 ns supported the stability of 16 within the binding pocket. Largely, our results supported that this novel compound 16 binds with domains I and II, and the domain II-III linker of the 3CLpro protein, suggesting its suitability as a strong candidate for therapeutic discovery against COVID-19.