We investigate the metal enrichment of the intracluster medium (ICM) within the framework of hierarchical models of galaxy formation. We calculate the formation and evolution of galaxies and clusters using a semi-analytical model which includes the effects of flows of gas and metals both into and out of galaxies. For the first time in a semi-analytical model, we calculate the production of both α and iron-peak elements based on theoretical models for the lifetimes and ejecta of type Ia and II supernovae (SNe Ia and II). It is essential to include the long lifetimes of the SNIa progenitors in order to correctly model the evolution of the iron-peak elements. We find that if all stars form with an initial mass function (IMF) similar to that found in the solar neighbourhood, then the metallicities of O, Mg, Si and Fe in the ICM are predicted to be two to three times lower than the observed values. In contrast, a model (also favoured on other grounds) in which stars formed in bursts triggered by galaxy mergers have a top-heavy IMF reproduces the observed ICM abundances of O, Mg, Si and Fe. The same model predicts ratios of ICM mass to total stellar luminosity in clusters which agree well with observations. According to our model, the bulk of the metals in clusters are produced by L* and brighter galaxies. We predict only mild evolution of [Fe/H] in the ICM with redshift out to z∼ 1, consistent with the sparse data available on high-z clusters. In contrast, the [O/Fe] ratio is predicted to gradually decrease with time because of the delayed production of iron compared with oxygen. We find that, at a given redshift, the scatter in global metallicity for clusters of a given mass is quite small, even though the formation histories of individual clusters show wide variations. The observed diversity in ICM metallicities may thus result from the range in metallicity gradients induced by the scatter in the assembly histories of clusters of galaxies.