In this paper, density functional theory (DFT) simulations are used to evaluate the possible use of a graphene oxide-based poly(ethylene glycol) (GO/PEG) nanocomposite as a drug delivery substrate for cephalexin (CEX), an antibiotic drug employed to treat wound infection. First, the stable configuration of the PEGylated system was generated with a binding energy of −25.67 kcal/mol at 1.62 Å through Monte Carlo simulation and DFT calculation for a favorable adsorption site. The most stable configuration shows that PEG interacts with GO through hydrogen bonding of the oxygen atom on the hydroxyl group of PEG with the hydrogen atom of the carboxylic group on GO. Similarly, for the interaction of the CEX drug with the GO/PEG nanocomposite excipient system, the adsorption energies are computed after determining the optimal and thermodynamically favorable configuration. The nitrogen atom from the amine group of the drug binds with a hydrogen atom from the carboxylic group of the GO/PEG nanocomposite at 1.75 Å, with an adsorption energy of −36.17 kcal/mol, in the most stable drug–excipient system. Drug release for tissue regeneration at the predicted target cell is more rapid in moist conditions than in the gas phase. The solubility of the suggested drug in the aqueous media around the open wound is shown by the magnitude of the predicted solvation energy. The findings from this study theoretically validate the potential use of a GO/PEG nanocomposite for wound treatment application as a drug carrier for sustained release of the CEX drug.