This work concerns the search for new ways to modify the surface of the biomedical Ti–13Zr–13Nb alloy for applications in regenerative medicine and personalized medicine. Obtained for the first time, oxide nanotubes (ONTs) layers of first-generation (1G) on a Ti–13Zr–13Nb alloy were produced by anodizing in 0.5% HF electrolyte at 20 V for 120 min. The physico-chemical characterization of the obtained bamboo-inspired 1G ONTs was conducted using TEM and ATR-FTIR methods. In vitro corrosion resistance of the 1G ONTs and comparative Ti–13Zr–13Nb substrate in saline solution at 37 °C was conducted by open-circuit potential, Tafel curves, anodic polarization curves, and EIS methods. LEIS and SVET study of local corrosion resistance was also carried out. It was found that surface modification by anodizing of the Ti–13Zr–13Nb alloy under proposed conditions allowed to obtain porous ONTs highly resistant to pitting corrosion. The obtained results give a new insight into the relationship between the morphological parameters of first-generation oxide nanotubes and in vitro corrosion resistance of the Ti–13Zr–13Nb alloy in saline solution at the macro- and microscale.