We investigate the [3.6]-[4.5] Spitzer-IRAC colour behaviour of the early-type galaxies of the SAURON survey, a representative sample of 48 nearby ellipticals and lenticulars. We investigate how this colour, which is unaffected by dust extinction, can be used to constrain the stellar populations in these galaxies. We find a tight relation between the [3.6]-[4.5] colour and effective velocity dispersion, a good mass indicator in early-type galaxies: ([3.6]-[4.5])e = (-0.109 ? 0.007)?+ (0.154 ? 0.016). Contrary to other colours in the optical and near-infrared, we find that the colours become bluer for larger galaxies. The relations are tighter when using the colour inside re (scatter 0.013 mag), rather than the much smaller re/8 aperture (scatter 0.023 mag), due to the presence of young populations in the central regions. We also obtain strong correlations between the [3.6]-[4.5] colour and three strong absorption lines (H?, Mgb and Fe 5015). Comparing our data with the models of Marigo et al., which show that more metal rich galaxies are bluer, we can explain our results in a way consistent with results from the optical, by stating that larger galaxies are more metal rich. The blueing is caused by a strong CO absorption band, whose line strength increases strongly with decreasing temperature and which covers a considerable fraction of the 4.5-?m filter. In galaxies that contain a compact radio source, the [3.6]-[4.5] colour is generally slightly redder (by 0.015 ? 0.007 mag using the re/8 aperture) than in the other galaxies, indicating small amounts of either hot dust, non-thermal emission, or young stars near the centre. We find that the large majority of the galaxies show redder colours with increasing radius. Removing the regions with evidence for young stellar populations (from the H? absorption line) and interpreting the colour gradients as metallicity gradients, we find that our galaxies are more metal poor going outwards. The radial [3.6]-[4.5] gradients correlate very well with the metallicity gradients derived from optical line indices. We do not find any correlation between the gradients and galaxy mass; at every mass, galaxies display a real range in metallicity gradients. Consistent with our previous work on line indices, we find a tight relation between local [3.6]-[4.5] colour and local escape velocity. The small scatter from galaxy to galaxy, although not negligible, shows that the amount and distribution of the dark matter relative to the visible light cannot be too different from galaxy to galaxy. Due to the lower sensitivity of the [3.6]-[4.5] colour to young stellar populations, this relation is more useful to infer the galaxy potential than the Mgb-vesc relation.