Over the past decade, several works have used the ratio between total (rest 8-1000 mu m) infrared and radio (rest 1.4 GHz) luminosity in star-forming galaxies (q(IR)), 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 q(IR) with redshift, finding a mild but significant decline that is yet to be understood. Here, for the first time, we calibrate q(IR) as a function of both stellar mass (M-star) and redshift, starting from an M-star-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-star,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-star, with more massive galaxies displaying a systematically lower q(IR). A secondary, weaker dependence on redshift is also observed. The best-fit analytical expression is the following: q(IR)(M-star, z) = (2.646 +/- 0.024) x (1+z)((-0.023 +/- 0.008))-(0.148 +/- 0.013) x (log M-star/M-circle dot-10). Adding the UV dust-uncorrected contribution to the IR as a proxy for the total SFR would further steepen the q(IR) dependence on M-star. We interpret the apparent redshift decline reported in previous works as due to low-M-star 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-star-dependent recipes that will enable us to convert detections from future ultra-deep radio surveys into accurate SFR measurements down to low-M-star galaxies with low SFR.