Over the past decade, several works have used the ratio between total (rest 8‒1000 μm) infrared and radio (rest 1.4 GHz) luminosity in star-forming galaxies (qIR), often referred to as the infrared-radio correlation (IRRC), to calibrate the radio emission as a star formation rate (SFR) indicator. Previous studies constrained the evolution of qIR with redshift, finding a mild but significant decline that is yet to be understood. Here, for the first time, we calibrate qIR as a function of both stellar mass (M⋆) and redshift, starting from an M⋆-selected sample of > 400 000 star-forming galaxies in the COSMOS field, identified via (NUV ‒ r)/(r ‒ J) colours, at redshifts of 0.1 < z < 4.5. Within each (M⋆,z) bin, we stacked the deepest available infrared/sub-mm and radio images. We fit the stacked IR spectral energy distributions with typical star-forming galaxy and IR-AGN templates. We then carefully removed the radio AGN candidates via a recursive approach. We find that the IRRC evolves primarily with M⋆, with more massive galaxies displaying a systematically lower qIR. A secondary, weaker dependence on redshift is also observed. The best-fit analytical expression is the following: qIR(M⋆, z) = (2.646 ± 0.024) × (1 + z)( ‒ 0.023 ± 0.008)-(0.148 ± 0.013) × (log M⋆/M⊙ ‒ 10). Adding the UV dust-uncorrected contribution to the IR as a proxy for the total SFR would further steepen the qIR dependence on M⋆. We interpret the apparent redshift decline reported in previous works as due to low-M⋆ galaxies being progressively under-represented at high redshift, as a consequence of binning only in redshift and using either infrared or radio-detected samples. The lower IR/radio ratios seen in more massive galaxies are well described by their higher observed SFR surface densities. Our findings highlight the fact that using radio-synchrotron emission as a proxy for SFR requires novel M⋆-dependent recipes that will enable us to convert detections from future ultra-deep radio surveys into accurate SFR measurements down to low-M⋆ galaxies with low SFR.