Wide-field JHKs near-infrared observations covering an area of 1.8◦ × 1.8◦ centred on M33 were obtained using WFCAM at UKIRT. These data show a large population of intermediate-age asymptotic giant branch (AGB) stars. Aims. We have used both C-type and M-type AGB stars to determine spatial variations in metallicity and mean age across the galaxy. Methods. We distinguished between C-type and M-type AGB stars from their location in the colour-magnitude diagram (J − Ks, Ks). The distribution of these stars is supported by a cross-identification between our sample and a catalogue of optically confirmed, long-period variable stars, as well as with the list of sources detected by Spitzer in the mid-infrared. We calculated the C/M ratio and the orientation of the galaxy in the sky, and compared the Ks magnitude distribution with theoretical distributions spanning a range of metallicities and star formation rates (SFRs). Results. The C/M ratio surface map confirms a metallicity gradient in the galaxy corresponding to a spread in [Fe/H] = 0.6 dex with substructures in the inner and outer galaxy. Magnitude and colour variations suggest orientation and extinction effects on the galaxy disc. Maps showing the distribution of mean age and metallicity obtained from the Ks method suggest that: the outer galaxy disc/halo is metal poorer than the nuclear region and metal-rich clumps in the inner galaxy change location with time. The average outer ring and nuclear stellar population is ∼6 Gyr old while central regions are a few Gyr younger.