Context. The infrared-radio correlation (IRRC) of star-forming galaxies can be used to estimate their star formation rate (SFR) based on the radio continuum luminosity at MHz-GHz frequencies. For its practical application in future deep radio surveys, it is crucial to know whether the IRRC persists at high redshift z.|Aims. Previous works have reported that the 1.4 GHz IRRC correlation of star-forming galaxies is nearly z-invariant up to z approximate to 4, but depends strongly on the stellar mass M-star. This should be taken into account for SFR calibrations based on radio luminosity.|Methods. To understand the physical cause behind the M-star dependence of the IRRC and its properties at higher z, we constructed a phenomenological model for galactic radio emission. Our model is based on a dynamo-generated magnetic field and a steady-state cosmic ray population. It includes a number of free parameters that determine the galaxy properties. To reduce the overall number of model parameters, we also employed observed scaling relations.|Results. We find that the resulting spread of the infrared-to-radio luminosity ratio, q(z, M-star), with respect to M-star is mostly determined by the scaling of the galactic radius with M-star, while the absolute value of the q(z, M-star) curves decreases with more efficient conversion of supernova energy to magnetic fields and cosmic rays. Additionally, decreasing the slope of the cosmic ray injection spectrum, alpha(CR), results in higher radio luminosity, decreasing the absolute values of the q(z, M-star) curves. Within the uncertainty range of our model, the observed dependence of the IRRC on M-star and z can be reproduced when the efficiency of supernova-driven turbulence is 5%, 10% of the kinetic energy is converted into magnetic energy, and alpha(CR) approximate to 3.0.|Conclusions. For galaxies with intermediate to high (M-star approximate to 10(9.5) - 10(11) M-circle dot) stellar masses, our model results in an IRRC that is nearly independent of z. For galaxies with lower masses (M-star approximate to 108.5 M-circle dot), we find that the IR-to-radio flux ratio increases with increasing redshift. This matches the observational data in that mass bin which, however, only extends to z approximate to 1.5. The increase in the IR-to-radio flux ratio for low-mass galaxies at z greater than or similar to 1.5 that is predicted by our model could be tested with future deep radio observations.