We present an analysis of the galaxy stellar mass function (SMF) of 14 known protoclusters between 2.0 < z < 2.5 in the COSMOS field, down to a mass limit of 10(9.5) M⊙. We use existing photometric redshifts with a statistical background subtraction, and consider star-forming and quiescent galaxies identified from (NUV - r) and (r - J) colours separately. Our fiducial sample includes galaxies within 1 Mpc of the cluster centres. The shape of the protocluster SMF of star-forming galaxies is indistinguishable from that of the general field at this redshift. Quiescent galaxies, however, show a flatter SMF than in the field, with an upturn at low mass, though this is only significant at similar to ∼2σ. There is no strong evidence for a dominant population of quiescent galaxies at any mass, with a fraction <15 per cent at 1σ confidence for galaxies with log M*/M⊙ < 10.5. We compare our results with a sample of galaxy groups at 1 < z < 1.5, and demonstrate that a significant amount of environmental quenching must take place between these epochs, increasing the relative abundance of high-mass (M* > 10^(10.5)M⊙) quiescent galaxies by a factor greater than or similar to 2. However, we find that at lower masses (M* < 10^(10.5)M⊙), no additional environmental quenching is required.