We present a detailed investigation of the effects imprinted by a direct interaction between dark energy and cold dark matter particles on the halo mass function of groups and clusters of galaxies. Making use of the public halo catalogues of the CoDECS simulations, we derive the halo mass function for several different types of coupled dark energy scenarios, based on both the friends-of-friends algorithm and the spherical overdensity halo identification for different values of the overdensity threshold Δc. We compare the computed halo mass functions for coupled dark energy cosmologies with ΛCDM as well as with the predictions of the standard analytic fitting functions. Our results show that the standard fitting functions still reproduce both the friends-of-friends and spherical overdensity halo mass functions of interacting dark energy cosmologies reasonably well at intermediate masses and low redshifts, once rescaled to the characteristic amplitude of linear density perturbations of each specific model as given by σ8. However, we also find that such apparent degeneracy with σ8 is broken by both the high-mass tail and the redshift evolution of our halo mass functions, with deviations beyond ˜10 per cent for most of the models under investigation. Furthermore, the discrepancy with respect to the predictions of standard fitting functions rescaled with the characteristic value of σ8 shows - for some models - a strong dependence on the spherical overdensity threshold Δc used for the halo identification. We find that such an effect is due to a significant increase of halo concentration at low redshifts in these models that is, however, absent in the majority of the cosmological scenarios considered in this work. We can therefore conclude that the universality of the halo mass function is violated by cosmological models that feature a direct interaction between dark energy and cold dark matter.