Urea is a molecule of great interest in chemistry and biology. In particular, it is considered a key building block in prebiotic chemistry on Earth. The hypothesis of its possible exogenous origin has been reinforced after the recent detection of this molecule in the interstellar medium, where it is believed to form in the ice mantles of dust grains. In this work the infrared spectra of urea ices and urea:H2O ice mixtures have been studied both experimentally and theoretically. Urea ices were generated by vapour deposition at temperatures between 10 K and 270 K. It was found that an amorphous phase is formed at temperatures below 200 K. A theoretical modelling of crystalline urea and of a tentative amorphous urea solid phase, as well as of amorphous urea:H2O ice mixtures, has been performed. The corresponding infrared spectra were simulated with density functional theory. The main spectral features observed in the various solid samples are interpreted with the help of the theoretical results. Infrared band strengths are also provided for amorphous and crystalline urea. The infrared spectroscopic information given in this work is expected to be useful for the detection and quantification of urea in astrophysical ices.