Nitrogen-doped multi-walled carbon nanotubes (N-MWCNTs) are widely used for drug delivery. One of the main challenges is to clarify their interaction with hypoxia-inducible factor 1 alpha (HIF-1α), the lack of which leads to oncological and cardiovascular diseases. In the presented study, N-MWCNTs were synthesized by catalytic chemical vapor deposition and irradiated with argon ions. Their chemical state, local structure, interfaces, Stone–Wales defects, and doping with nitrogen were analyzed by high resolution transmission electron microscopy (HRTEM), Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. Using experimental data, supercells of functionalized N-MWCNTs with an oxygen content of 2.7, 4 and 6 at. % in carboxyl groups were built by quantum chemical methods. Our analysis by the self-consistent charge density functional tight-binding (SCC DFTB) method shows that a key role in the functionalization of CNTs with carboxyl groups belongs to Stone–Wales defects. The results of research in the decoration of CNTs with HIF-1α demonstrate the possibility of wave-diffusion drug delivery. The nature of hybridization and relaxation determines the mechanism of oxygen regulation with HIF-1α molecules, namely, by OH-(OH–C) and OH-(O=C) chemical bonds. The concentration dependence of drug release in the diffusion mode suggests that the best pattern for drug delivery is provided by the tube with a carboxylic oxygen content of 6 at. %.