This article compares the Ks magnitude distribution of Small Magellanic Cloud asymptotic giant branch stars obtained from the DENIS and 2MASS data with theoretical distributions. Methods. Theoretical Ks magnitude distributions have been constructed using up-to-date stellar evolution calculations for low- and intermediate-mass stars, and in particular for thermally pulsing asymptotic giant branch stars. Separate fits of the magnitude distributions of carbon- and oxygen-rich stars allowed us to constrain the metallicity distribution across the galaxy and its star formation rate. Results. The Small Magellanic Cloud stellar population is found to be on average 7−9 Gyr old but older stars are present at its periphery and younger stars are present in the direction of the companion galaxy the Large Magellanic Cloud. The metallicity distribution traces a ring-like structure that is more metal rich than the inner region of the galaxy. Conclusions. The C/M ratio discussed in Paper I is a tracer of the metallicity distribution only if the underlying stellar population is of intermediate-age.