Observations show that galaxies follow a mass-metallicity relation over a wide range of masses. One currently favoured explanation is that less massive galaxies are less able to retain the gas and stellar ejecta and thus may lose the freshly produced metals in the form of galactic outflows. Galaxies with a low current star formation rate have been found to contain star clusters up to a lower mass limit. Since stars are predominately born in clusters, and less massive clusters have been found to be less likely to contain very massive stars, this implies that in environments or at times of low star formation, the stellar initial mass function does not extend to as high masses as during high star formation epochs. It is found that the oxygen yield is reduced by a factor of 30 when the star formation rate is decreased by 3 to 4 orders of magnitude. With this concept, chemical evolution models for galaxies of a range of masses are computed and shown to provide an excellent fit to the mass-metallicity relation derived recently by Tremonti et al. Furthermore, the models match the relation between galaxy mass and effective yield. Thus, the scenario of a variable integrated stellar initial mass function, which is based on the concept of formation of stars in clusters, may offer an attractive alternative or partial explanation of the mass-metallicity relation in galaxies.