Neodymium (Nd)-doped ZnO nanostructures with different amounts of Nd were obtained by the electrospinning–calcination method. X-ray diffraction measurements indicated that the prepared nanostructures have a wurtzite structure without undesirable impurities. Nd doping changes the mean crystallite size as well the lattice strain, as proved by Williamson–Hall plots. The ZnO-based nanostructures were tested as photocatalysts for methylene blue (MB) dye and ciprofloxacin (CIP) drug pollutant degradations under visible light irradiation. Corroborating the obtained results, it was found that the reaction rate constant increased almost linearly with the mean crystallite size (from 2.235 × 10⁻² to 3.482 × 10⁻² min⁻¹) with a variation in the mean crystallite size from 24.2 to 42.1 nm. Furthermore, the best catalyst sample (0.1% Nd-doped ZnO) was used to optimize the photodegradation process of ciprofloxacin, taking into account the pollutant concentration as well as the catalyst dose. The removal efficiency after 120 min was about 100%, with the rate constant of k = 5.291·10⁻² min⁻¹ (CIP) and k = 4.780·10⁻² min⁻¹ (MB) for the established optimal conditions. Considering the value of the rate constant, the half-life of the reaction (τ_1/2 = ln2/k) was evaluated to be about τ_1/2 =13 min for CIP and 14.5 min corresponding to MB. Several catalytic cycles were successfully performed without any loss of photocatalytic activity using these nanostructures, demonstrating that the obtained nanostructures have good stability in the leaching processes.