High-strength TiHfZrNbx high-entropy alloys could become the ideal materials for small-diameter endovascular stents once their corrosion resistance in the physiological milieu is confirmed. This work aims at evaluating the corrosion resistance of a TiHfZrNbx high-entropy-alloys family in Hanks’ solution at 37 °C and revealing the influence of niobium on the mechanisms of dissolution and passivation. The alloys were subjected to a series of static and dynamic electrochemical tests and surface characterization, employing the static/dynamic/cyclic polarizations, impedance spectroscopy, XPS, AFM, and SEM. Results confirm a higher corrosion resistance of the alloys compared to that of CP-Ti and Ti6Al4V. The addition of niobium considerably improves the microstructural homogeneity that ensures a low dissolution rate and a greater resistance of the film due to the lower concentration of point defects. The passive film behaves as an n-type semiconductor and is composed of a mixture of TiO2, Nb2O5, ZrO2, and HfO2 oxides, with the presence of metallic hydroxides on the outermost layer. A detailed description of the niobium influence on the mechanisms of the dissolution and passivation is presented in this work.