To reduce the direct side effects of chemotherapy, researchers are trying to establish a new approach of a drug-delivery system using nanomaterials. In this study, we investigated graphene and its derivative nanomaterials for their favorable adsorption behavior with the anti-cancer drug hydroxyurea (HU) using DFT calculations. Initially, different pristine and doped graphene and its derivatives were taken into consideration as HU drug carriers. Among them, AlN, GaN, GaN-doped AlN, and AlN-doped GaN nanosheets exhibited favorable adsorption behavior with HU. The HU adsorbed on these four nanosheets with adsorption energies of −0.92, −0.75, −0.83, and −0.69 eV, transferring 0.16, 0.032, 0.108, and 0.230 e charges to the nanosheets, respectively, in air medium. In water solvent media, these four nanosheets interacted with HU by −0.56, −0.45, −0.58, and −0.56 eV by accepting a significant amount of charge of about 0.125, 0.128, 0.192, and 0.126 e from HU. The dipole moment and COSMO analysis also indicated that these nanosheets, except for GaN-doped AlN, show high asymmetricity and solubility in water solvent media due to the increased values of the dipole moment by two or three times after the adsorption of the HU drug. Quantum molecular descriptors also suggest that the sensitivity and reactivity of the nanosheets are enhanced during the interaction with HU. Therefore, these nanosheets can be used as anti-cancer drug carriers.