The dual-specificity tyrosine phosphorylation-regulated kinase 1A (DYRK1A) is a novel, promising and emerging biological target for therapeutic intervention in neurodegenerative diseases, especially in Alzheimer’s disease (AD). The molMall database, comprising rare, diverse and unique compounds, was explored for molecular docking-based virtual screening against the DYRK1A protein, in order to find out potential inhibitors. Ligands exhibiting hydrogen bond interactions with key amino acid residues such as Ile165, Lys188 (catalytic), Glu239 (gk+1), Leu241 (gk+3), Ser242, Asn244, and Asp307, of the target protein, were considered potential ligands. Hydrogen bond interactions with Leu241 (gk+3) were considered key determinants for the selection. High scoring structures were also docked by Glide XP docking in the active sites of twelve DYRK1A related protein kinases, viz. DYRK1B, DYRK2, CDK5/p25, CK1, CLK1, CLK3, GSK3β, MAPK2, MAPK10, PIM1, PKA, and PKCα, in order to find selective DYRK1A inhibitors. MM/GBSA binding free energies of selected ligand–protein complexes were also calculated in order to remove false positive hits. Physicochemical and pharmacokinetic properties of the selected six hit ligands were also computed and related with the proposed limits for orally active CNS drugs. The computational toxicity webserver ProTox-II was used to predict the toxicity profile of selected six hits (molmall IDs 9539, 11352, 15938, 19037, 21830 and 21878). The selected six docked ligand–protein systems were exposed to 100 ns molecular dynamics (MD) simulations to validate their mechanism of interactions and stability in the ATP pocket of human DYRK1A kinase. All six ligands were found to be stable in the ATP binding pocket of DYRK1A kinase.