Phosphoramides and their complexes are attractive compounds due to their significant inhibiting functionality in biological medicine. In this paper, a novel organotin(IV)-phosphoramide complex (Sn(CH3)2Cl2{[(3-Cl)C6H4NH]P(O)[NC4H8O]2}2, 1), derived from a reaction between phosphoric triamide ligand with dimethyltin dichloride, and a new amidophosphoric acid ester ([OCH2C(CH3)2CH2O]P(O)[N(CH3)CH2C6H5], 2), prepared from the condensation of a cyclic chlorophosphate reagent with N-methylbenzylamine, are structurally characterized and in silico investigated as potential SARS-CoV-2 and Monkeypox inhibitors by molecular docking simulation. Both compounds crystallize in the monoclinic crystal system with space group P21/c. The asymmetric unit of the complex 1 consists of one-half molecule, where SnIV is located on an inversion center, while the asymmetric part of 2 consists of one whole molecule. In the complex 1, the tin atom adopts a six-coordinate octahedral geometry with trans groups of (Cl)2, (CH3)2 and (PO)2 (PO = phosphoric triamide ligand). The molecular architecture consists of the N–H⋯Cl hydrogen bonds stretching as a 1D linear arrangement along the b axis with intermediate $R^2_2$ ring motifs, whereas in the case of 2, the crystal packing is devoid of any classical hydrogen bond interaction. Furthermore, a graphical analysis by using Hirshfeld surface method identifies the most important intermolecular interactions being of the type H⋯Cl/Cl⋯H (for 1) and H⋯O/O⋯H (for 1 and 2), covering the hydrogen bond interactions N–H⋯Cl and C–H⋯O═P, respectively, which turn out to be favoured. A biological molecular docking simulation on the studied compounds provides evidence to suggest a significant inhibitory potential against SARS-COV-2 (6LU7) and Monkeypox (4QWO) especially for 6LU7 with a binding energy around −6 kcal/mol competing with current effective drugs against this virus (with a binding energy around −5 and −7 kcal/mol). It is worth noting that this report is the first case of an inhibitory potential evaluation of phosphoramide compounds on Monkeypox.