ABSTRACT Simulations of cold dark matter make robust predictions about the slope and normalization of the dark matter halo and subhalo mass functions on small scales. Recent observational advances utilizing strong gravitational lensing have demonstrated the ability of this technique to place constraints on these quantities on subgalactic scales corresponding to dark matter halo masses of 106–$10^9\, \mathrm{M}_⊙$. On these scales the physics of baryons, which make up around 17 per cent of the matter content of the Universe but which are not included in pure dark matter N-body simulations, are expected to affect the growth of structure and the collapse of dark matter haloes. In this work, we develop a semi-analytic model to predict the amplitude and slope of the dark matter halo and subhalo mass functions on subgalactic scales in the presence of baryons. We find that the halo mass function is suppressed by up to 25 per cent, and the slope is modified, ranging from −1.916 to −1.868 in this mass range. These results are consistent with current measurements, but differ sufficiently from the expectations for a dark matter only universe that it may be testable in the near future.