We present results from a deep mid-infrared survey of the Hubble Deep Field South (HDF-S) region performed at 6.7 and 15μm with the ISOCAM instrument on board the Infrared Space Observatory (ISO ). We find reliable optical/near-infrared associations for 32 of the 35 sources detected in this field by Oliver et al. (Paper I): eight of them are identified as stars, one is definitely an active galactic nucleus (AGN), a second seems likely to be an AGN too, while the remaining 22 appear to be normal spiral or starburst galaxies. Using model spectral energy distributions (SEDs) of similar galaxies, we compare methods for estimating the star formation rates (SFRs) in these objects, finding that an estimator based on integrated (3-1000μm) infrared luminosity reproduces the model SFRs best. Applying this estimator to model fits to the SEDs of our 22 spiral and starburst galaxies, we find that they are forming stars at rates of ~1-100Msolar yr-1 , with a median value of ~40Msolar yr-1 , assuming an Einstein-de Sitter universe with a Hubble constant of 50kms-1 Mpc-1 , and star formation taking place according to a Salpeter initial mass function (IMF) across the mass range 0.1-100Msolar . We split the redshift range 0.0<=z <=0.6 into two equal-volume bins to compute raw estimates of the star formation rate density, ρ˙ *, contributed by these sources, assuming the same cosmology and IMF as above and computing errors based on estimated uncertainties in the SFRs of individual galaxies. We compare these results with other estimates of ρ˙ * made with the same assumptions, showing them to be consistent with the results of Flores et al. from their ISO survey of the CFRS 1415+52 field. However, the relatively small volume of our survey means that our ρ˙ * estimates suffer from a large sampling variance, implying that our results, by themselves, do not place tight constraints on the global mean star formation rate density.