Hybrid density functional theory calculations were performed for the first time on structure, stability, phonon frequencies, and thermodynamic functions of hafnia-based single-wall nanotubes. The nanotubes were rolled up from the thin free layers of cubic and tetragonal phases of HfO₂. It was shown that the most stable HfO₂ single-wall nanotubes can be obtained from hexagonal (111) layer of the cubic phase. Phonon frequencies have been calculated for different HfO₂ nanolayers and nanotubes to prove the local stability and to find the thermal contributions to their thermodynamic functions. The role of phonons in stability of nanotubes seems to be negligible for the internal energy and noticeable for the Helmholtz free energy. Zone folding approach has been applied to estimate the connection between phonon modes of the layer and nanotubes and to approximate the nanotube thermodynamic properties. It is found that the zone-folding approximation is sufficiently accurate for heat capacity, but less accurate for entropy. The comparison has been done between the properties of TiO₂, ZrO₂, and HfO₂.