The production cross sections of $^{68,69}$Ge and $^{66,67}$Ga by alpha-induced reactions on $^{nat}$Zn have been measured using the stacked-foil activation method and off-line gamma-ray spectrometry from their threshold energies to 50.7 MeV. The derived cross sections were compared with the previous experimental data and the calculated values in the TENLD-2017 library. Our result shows a slightly larger amplitude than the previous data at the peak, though the peak energy is consistent with them.