We present the study of the metallicity dependence of the Fourier amplitude ratios R21 and R31 for the light curves of short-period Galactic classical Cepheids in B, V, RC and IC bands. Based on the available photometric and spectroscopic data, we determined the relations between the atmospheric iron abundance, [Fe/H], and the Fourier parameters. Using these relations we calculated the photometric [Fe/H] values of all programme Cepheids with an average accuracy of +/-0.15dex. No spectroscopic iron abundance was known before for 14 of these stars. These empirical results provide an alternate method to determine the iron abundance of classical Cepheids too faint for spectroscopic observations. We also checked whether the metal-poor Cepheids of both Magellanic Clouds follow the same relationships, and a good agreement was found. (1 data file).