Aims. Archival observations of infrared fine-structure lines of the young Galactic supernova remnant Cassiopeia A allow us to test existing models and determine the physical parameters of various regions of the fast-moving knots, which are metal-dominated clouds of material ejected by the supernova explosion. Spitzer data are used to determine the fluxes of the O, Ne, Si, S, Ar, and Fe ion fine-structure lines originating in the fast-moving knots. The ratios of these line fluxes are used as plasma diagnostics. We also determine the infrared line flux ratios with respect to the optical [O iii] 5007 Å line in the knots with previously measured reddening. Additionally, we analyze several optical and near-infrared observations of the fast-moving knots to obtain clearer insight into the post-shock photoionized region structure. Results. We show that the infrared oxygen line flux predictions of all existing theoretical models are correct only to within a factor of a several. Comparison of the model predictions shows that to reproduce the observations it is essential to include the effects of the electron conductivity and dust. Detailed analysis of the diagnostic line flux ratios of various ions allows us to qualitatively confirm the general model of fast-moving knot emission and determine observationally for the first time the physical conditions in the photoionized region after the shock. We infer from the [O iii] line flux ratios that the pre-shock cloud densities are higher than assumed in existing theoretical models and most probably correspond to several hundred particles per cm 3 . We also determine the Cas A luminosity in the infrared continuum and lines. We show that accounting for the charge exchange processes in the post-shock photoionized region allows us to reproduce most of the relevant spectral line ratios even in the frame of a single-temperature model of this region. We also estimate its plasma parameters, thickness, and carbon abundance.