We used models of thermally pulsing asymptotic giant branch (AGB) stars, which also describe the dust-formation process in the wind, to interpret the combination of near- and mid-infrared photometric data of the dwarf galaxy IC 1613. This is the first time that this approach is extended to an environment different from the Milky Way and the Magellanic Clouds (MCs). Our analysis, based on synthetic population techniques, shows nice agreement between the observations and the expected distribution of stars in the colour-magnitude diagrams obtained with JHK and Spitzer bands. This allows a characterization of the individual stars in the AGB sample in terms of mass, chemical composition and formation epoch of the progenitors. We identify the stars exhibiting the largest degree of obscuration as carbon stars evolving through the final AGB phases, descending from 1-1.25 M⊙ objects of metallicity Z = 10-3 and from 1.5-2.5 M⊙ stars with Z = 2 × 10-3. Oxygen-rich stars constitute the majority of the sample (˜65 per cent), mainly low-mass stars (<2 M⊙) that produce a negligible amount of dust (≤10-7 M⊙ yr-1). We predict the overall dust-production rate from IC 1613, mostly determined by carbon stars, to be ˜6 × 10-7 M⊙ yr-1 with an uncertainty of 30 per cent. The capability of the current generation of models to interpret the AGB population in an environment different from the MCs opens the possibility to extend this kind of analysis to other Local Group galaxies.