Star-forming clumps dominate the rest-frame ultraviolet morphology of galaxies at the peak of cosmic star formation. If turbulence driven fragmentation is the mechanism responsible for their formation, we expect their stellar mass function to follow a power law of slope close to -2. We test this hypothesis performing the first analysis of the stellar mass function of clumps hosted in galaxies at z similar to 1-3.5. The clump sample is gathered from the literature with similar detection thresholds and stellar masses determined in a homogeneous way. To overcome the small number statistics per galaxy (each galaxy hosts up to a few tens of clumps only), we combine all high-redshift clumps. The resulting clump mass function follows a power law of slope similar to-1.7 and flattens at masses below 2 x 10(7) M-circle dot. By means of randomly sampled clump populations, drawn out of a power-law mass function of slope -2, we test the effect of combining small clump populations, detection limits of the surveys, and blending on the mass function. Our numerical exercise reproduces all the features observed in the real clump mass function confirming that it is consistent with a power law of slope similar or equal to-2. This result supports the high-redshift clump formation through fragmentation in a similar fashion as in local galaxies, but under different gas conditions.