We address the origin of the ‘downsizing’ of elliptical galaxies, according to which the stars in more massive galaxies formed earlier and over a shorter period than those in less massive galaxies. We show that this could be the natural result of a shutdown of star formation in dark matter haloes above a critical mass of ∼1012 M⊙. This is demonstrated using a semi-analytic simulation of galaxy formation within the standard hierarchical scenario of structure formation. The assumed threshold mass is motivated by the prediction of stable shock heating above this mass and the finding that such a shutdown reproduces the observed distribution of galaxies in luminosity and colour. The shutdown at a critical halo mass introduces a characteristic stellar mass for the transition of galaxies into the ‘red sequence’ of the galaxy colour–magnitude diagram. Central galaxies of haloes that are more massive today have reached this mass earlier and can therefore grow further along the red sequence by dry mergers, ending up more massive and containing older stars. Small galaxies formed in haloes below the critical mass can shutdown late, when they fall into haloes above the critical mass and become satellites. While our semi-analytic simulation that incorporates an explicit shutdown reproduces downsizing as inferred from the stellar ages of ellipticals, we explain why it is much harder to detect downsizing using the mass functions of different galaxy types.