Hafnia-based nanostructures and other high-k dielectrics are promising wide-gap materials for developing new opto- and nanoelectronic devices. They possess a unique combination of physical and chemical properties, such as insensitivity to electrical and optical degradation, radiation damage stability, a high specific surface area, and an increased concentration of the appropriate active electron-hole centers. The present paper aims to investigate the structural, optical, and luminescent properties of anodized non-stoichiometric HfO2 nanotubes. As-grown amorphous hafnia nanotubes and nanotubes annealed at 700 °C with a monoclinic crystal lattice served as samples. It has been shown that the bandgap Eg for direct allowed transitions amounts to 5.65 ± 0.05 eV for amorphous and 5.51 ± 0.05 eV for monoclinic nanotubes. For the first time, we have studied the features of intrinsic cathodoluminescence and photoluminescence in the obtained nanotubular HfO2 structures with an atomic deficiency in the anion sublattice at temperatures of 10 and 300 K. A broad emission band with a maximum of 2.3–2.4 eV has been revealed. We have also conducted an analysis of the kinetic dependencies of the observed photoluminescence for synthesized HfO2 samples in the millisecond range at room temperature. It showed that there are several types of optically active capture and emission centers based on vacancy states in the O3f and O4f positions with different coordination numbers and a varied number of localized charge carriers (V0, V−, and V2−). The uncovered regularities can be used to optimize the functional characteristics of developed-surface luminescent media based on nanotubular and nanoporous modifications of hafnia.