A comparative study of the electrochemical behavior of various forms of the antitumor antibiotic doxorubicin (DOX) - free and encapsulated in micelle-like nanoparticles of the biocompatible amphiphilic copolymer N-vinylpyrrolidone (VP) — methacrylic acid — triethylene glycol dimethacrylate (TEGDM) — in aqueous neutral buffer solutions on a glassy carbon electrode was carried out. The hydrodynamic radii of the Rh copolymer and DOX polymer nanostructures were determined using the dynamic light scattering method. It was demonstrated using cyclic and square wave voltammetry the presence of two main redox transitions for both forms of DOX at pH 7.24: irreversible oxidation/reduction in the potential range from 0.2 to 0.6 V and reversible reduction/reoxidation — from −0.4 to −0.7 V (saturated Ag/AgCl reference electrode), and their redox potentials were determined. The difference in the potentials of the corresponding peaks of both redox transitions does not exceed several tens (20–30) mV, while the oxidation of the encapsulated form is easier than the free one, and reduction is somewhat more difficult. Analysis of the dependence of the reduction current of both forms of DOX on the rate of potential sweep shows that electron transfer to a molecule of free DOX is largely determined by the rate of accumulation of the reagent in the adsorption layer, and the encapsulated form is characterized by mixed adsorption-diffusion control. Based on voltammetric data and the results of quantum chemical modeling, it was concluded that a hydrogen bond is formed between the oxygen-containing groups of the monomer units of the copolymer and the H-atoms OH and NH2 groups of DOX. The bond energies in the structures considered are calculated and it is shown that their values are close to classical ones if the carbonyl group of the lactam ring of VP in the encapsulating polymer is an electron donor, and the hydrogens OH and NH2 groups of DOX are acceptors. At the same time, the bonds formed with the participation of the oxygen atom of the ester group of the TEGDM unit are extremely weak.